T  H 


UC-NRLF 


B    3    ESS    D3fl 


GODFREY 


BUILDINGS 


STEEL  AND  REINFORCED  CONCRETE 
IN  BUILDINGS 

-BY- 

EDWARD  GODFREY,  M.  Am.  Soc.  C.  E. 

STRUCTURAL  ENGINEER  FOR 


ROBERT  IA£.  MVJNT  &  OO. 

CHICAGO         NEW  YORK         PITTSBURG         LONDON 


—AUTHOR    OF- 

Structural  Engineering  Book  I, 

TABLES 
I 

Structural  Engineering  Book  II, 

CONCRETE 

Structural  Engineering  Book  III, 

STEEL  DESIGNING 

(In  Manuscript) 

A  MINORITY  REPORT  ON  THE  QUEBEC  "BRIDGE  DISASTER 

(Pamphlet) 

SOME  MOQTED  QUESTIONS  IN  REINFORCED  CONCRETE 
DESIGN 

(Paper  Betore  Am.  Soc.  C,  E.) 


PRICE  $2.00  - 


Copyright   191  1   by 

EDWARD  GODFREY 


CONTENTS 


INTRODUCTION    ................................  1 

CHAPTER  I.—  FOUNDATIONS    .......................  3 

CHAPTER  II.—  FOOTINGS    ..........................  7 

CHAPTER  III.—  COLUMN  BASES   ...................  14 

CHAPTER  IV.—  COLUMNS  AND  OTHER  COMPRESSION 

MEMBERS    .......................  16 

WOODEN  COLUMNS  ................  17 

CAST  IRON   COLUMNS  ...............  20 

STEEL  COLUMNS   ...................  25 

REINFORCED  CONCRETE  COLUMNS  ____  30 

COLUMN  TABLES  ..................  34-46 

CHAPTER  V.—  LINTELS    .................  ..........      47 

CHAPTER  VI.—  BEAMS    ...........................      49 

WOODEN  BEAMS   ...................      49 

CAST  IRON  BEAMS  .................      50 

STEEL  BEAMS    .....................      51 

STEEL  BEAM  TABLES  ...............  58-60 

REINFORCED  CONCRETE  BEAMS  .......      61 

REINFORCED  CONCRETE  BEAM  TABLES.69-74 

CHAPTER  VII.—  GIRDERS    ..........................      75 

PLATE  GIRDERS  ....................      80 

PLATE  GIRDER  TABLES  ..............  81-82 

Box  GIRDER  TABLE  .................      90 

CHAPTER  VIII.—  TRUSSES    .........  .'  ..............      93 

TRUSS  DIAGRAMS   ................  98-112 

TENSION  MEMBERS   ................    113 

COMPRESSION   MEMBERS    ............    1  16 

TRUSS  MEMBERS  IN  BENDING  .......    116 

CHAPTER  IX.—  FLOOR  ARCHES  AND  '  SLABS  ..........    121 

REINFORCED  CONCRETE  SLABS  ........    123 

CHAPTER  X.—  STRUCTURAL  DETAILS    ...............  127 

RIVETS    ............................  127 

BOLTS    ............................  128 

SPLICES    ...........................  130 

END  CONNECTIONS  OF  BEAMS  .......  131 

END  CONNECTIONS  OF  GIRDERS  ____  ..  132 

DETAILS  OF  TIMBER  TRUSSES  ........  134 

CHAPTER  XI.—  ESTIMATING  LOADS  .  140 


INTRODUCJICN. 

The  purpose  of  this  book  is  to  supply  a  want  in  work 
where  designing  is  done  on  a  small  scale  that  does  not 
justify  the  employment  of  an  engineer.  A  large  amount 
of  this  sort  of  designing  is  done,  and  very  much  of  it  is 
faulty.  While  it  may  be  to  the  interest  of  the  author  and 
his  class  to  discourage  designing  on  the  part  of  men 
whose  training  does  not  fit  them  to  do  it  more  intelli- 
gently, the  fact  remains  that  the  work  is  done  and  will 
be  done,  and  done  very  often  by  men  who  do  not  un- 
derstand much  about  the  principles  of  proper  design. 
The  aim  in  writing  this  book  is  to  lay  down  the  princi- 
ples of  correct  and  consistent  design  as  applied  to  build- 
ings, and  to  give  simple  rules  and  tables  to  be  used  in 
designing. 

Architects'  designs  for  structural  work  of  any  magni- 
tude should,  of  course,  be  checked  by  a  structural  en- 
gineer. The  fee  for  this  is  less  than  for  making  an  orig- 
inal design  and  may  be  included  in  the  price  of  inspec- 
tion. The  checking  of  the  details  is  another  matter  that 
can  be  best  handled  by  a  structural  engineer :  this  can 
also  be  covered  in  a  contract  for  the  inspection  of  the 
steel  work. 

It  is  the  author's  intention,  while  indicating  what  may 
be  safely  done  by  one  not  thoroughly  conversant  with 
structural  design,  to  indicate  also,  by  the  contents  of  the 
book,  the  line  beyond  which  such  a  one  ventures  at  his 
peril  and  to  the  jeopardy  of  life  and  property. 

Bracing  of  buildings,  while  it  is  a  matter  of  utmost 
importance,  has  been  omitted  from  this  book,  for  the 
reason  that  it  is  an  engineering  problem  and  one  that 
can  scarcely  be  standardized.  In  the  majority  of  build- 
ings bracing  or  stiffness  is  supplied  by  the  walls.  High 
or  narrow  buildings  should  be  braced.  The  system  of 


bracing  is  a  ma-ter  requiring  special  consideration, 
a  matter  for  judgment  and  calculation  and  not  for 
standards. 

In  the  actual  proportioning  of  a  building  generally  the 
smaller  details  are  designed  first,  that  is,  the  floor  sys- 
tem is  decided  upon  first,  then  the  floor  beams  are  laid 
out,  and  their  sizes  as  well  as  those  of  the  girders  are 
determined.  Then  the  sections  of  the  columns  are  worked 
out,  and  when  the  load  on  the  base  of  a  column  is 
known,  the  pedestal  and  foundation  may  be  propor- 
tioned. In  this  book  the  reverse  order  will  be  adopted 
in  treating  these  parts,  beginning  with  the  foundation 
and  going  up  and  out  toward  the  smaller  details. 

While  this  book  is  designed  to  be  of  special  use  to 
architects  who  have  occasion  to  design  in  steel  and  re- 
inforced concrete,  it  is  believed  that  it  will  also  be  found 
useful  to  students  and  beginners  as  a  preliminary  to  the 
author's  more  complete  work  on  Steel  Designing.  There 
is  also  much  in  it  that  should  be  found  convenient  to 
structural  designers  in  all  lines. 

An  almost  necessary  accompaniment  to  this  book  is  a 
book  giving  the  dimensions  and  properties  of  steel  sec- 
tions, such  as  the  Carnegie  Pocket  Companion  or  God- 
frey's Tables. 


CHAPTER  I. 
Foundations. 

The  area  of  a  foundation  in  contact  with  the  soil  will 
depend  upon  the  bearing  power  of  the  soil.  This  bearing 
power  is  best  determined  by  experience  rather  than  ex- 
periment, though  in  some  cases  experiments  are  re- 
sorted to.  These  are  in  the  nature  of  a  test  load  applied 
on  a  certain  area  for  a  given  length  of  time.  There  are 
many  features  that  must  be  taken  into  consideration  in 
designing  a  foundation.  The  bearing  power  of  a  soil 
depends  not  only  upon  the  nature  of  the  soil  itself,  but 
also  upon  the  degree  of  confinement  of  the  soil.  The 
degree  of  confinement  will  be  gaged  largely  by  the  depth 
below  the  surface  to  which  the  trench  or  excavation  is 
made.  A  clay  that  might  stand  safely  two  tons  per 
square  foot  at  six  feet  below  the  surface  might  heave 
and  allow  the  same  load  to  sink,  if  the  trench  is  made 
only  a  foot  deep.  Moisture  in  a  soil  during  construction 
has  been  the  cause  of  disastrous  settlement.  Hence  drain- 
age at  such  a  time  is  of  prime  importance.  The  base- 
ment floor  of  a  building  during  construction  is  subject 
to  repeated  wetting,  and  may,  if  proper  care  is  not  taken, 
be  the  recipient  of  drainage  from  other  ground.  After 
completion  of  a  structure  the  basement  will  be  protected 
from  moisture  due  to  rains.  If  ground  water  is  not 
naturally  present,  the  soil  will  sustain  much  more  load. 

Another  feature  that  should,  if  possible,  be  taken  into 
consideration  in  planning  a  foundation  is  the  possibility 
of  excavation  in  close  proximity  to  the  foundation.  If 
excavation  is  made  near  a  foundation  carrying  a  heavy 
load,  and  if  that  excavation  extends  to  or  below  the 
level  of  the  foundation  in  question,  the  soil  may  flow  and 
allow  large  settlement  of  the  structure.  Thus,  excavating 
for  a  neighboring  building  or  a  vault  or  subway  may 
ieopardize  the  safety  of  a  building  that  otherwise  is  quite 
safe. 


Clay  soils  flow  readily  and  are  compressible.  Sandy 
soils  are  not  very  compressible,  but  they  will  flow  laterally, 
especially  when  wet,  if  not  confined.  Gravel  is  not  com- 
pressible and  is  not  so  apt  to  flow.  Mixtures  of  these  in 
varying  proportions  combine  the  properties  of  each.  Some 
clays,  if  kept  perfectly  dry,  will  bear  heavy  loads,  but  if 
wet,  become  like  putty.  Hence  assurance  that  clay  is  dry 
or  else  confined  is  of  great  importance. 

A  good  method  of  confining  the  soil  under  a  structure 
to  prevent  flow  is  to  drive  sheet  piling  around  it,  thus 
holding  the  soil  in  a  sort  of  box. 

As  far  as  practicable,  where  the  soil  is  of  a  uniform 
carrying  capacity,  the  pressure  per  square  foot  should  be 
constant  for  the  entire  structure.  Some  settlement  is  to 
be  expected,  and  it  is  important  that  this  settlement  be 
uniform  over  the  entire  foundation.  When  soils  of  dif- 
ferent compressibilities  are  met  with  in  the  same  building, 
such  as  clay  and  sand,  the  more  compressible  soil  should 
have  the  larger  footings. 

The  pressures  allowed,  by  the  New  York  Building  Code, 
per  square  foot  for  various  soils  are  as  follows :  Soft 
clay,  one  ton ;,  ordinary  clay  and  sand  together,  in  layers, 
wet  and  springy,  two  tons;  loam,  clay  or  fine  sand,  firm  and 
dry,  three  tons;  very  firm,  coarse  sand,  stiff  gravel  or 
hard  clay,  four  tons.  In  Baker's  Masonry  Construction 
the  following  are  given  as  the  safe  bearing  power  of  soils 
in  tons  per  square  foot:  Quicksand,  alluvial  soils,  etc., 
0.5  to  1 ;  sand,  clean  dry,  2  to  4 ;  sand,  compact  and  well 
cemented,  4  to  6;  gravel  and  coarse  sand,  well  cemented, 
8  to  10;  clay,  soft,  1  to  2;  clay  in  thick  beds,  moderately 
dry,  2  to  4;  clay  in  thick  beds,  always  dry,  4  to  6;  rock, 
from  5  up.  This  lower  value  is  for  rock  equal  to  poor 
brick  masonry.  In  case  of  hard  rock  the  area  of  foun- 
dation may  sometimes  be  determined  by  the  strength  of 
the  foundation  rather  than  that  of  the  rock.  Thus,  if 
concrete  is  used  in  a  pier  with  a  bearing  power  of  15 
tons  per  sq.  ft.,  this  sets  the  limit,  though  the  rock  may 
be  capable  of  carrying  a  greater  load. 


Sometimes  the  compressibility  of  the  soil  is  such  that  it  is 
impracticable  to  give  the  footing  the  spread  necessary  for 
the  load  to  be  carried.  Piles  may  then  be  driven  and  the 
load  supported  on  these.  Piles  are  sometimes  driven  to 
hard  bottom  and  sometimes  to  a  depth  that  results  in  a  cer- 
tain degree  of  refusal,  depending  in  such  cases  upon  fric- 
tion of  their  sides  for  their  supporting  power.  The  usual 
loads  allowed  on  wooden  piles -are  10  to  15  tons  per  pile. 
Sometimes  as  much  as  20  tons  is  allowed  on  a  pile.  Piles 
supported  by  friction  alone  should  not  be  loaded  so  heavily 
as  those  that  are  driven  to  hard  bottom.  Piles  are  gener- 
ally kept  2^/2  to  3  feet  apart  as  a  minimum. 

Wooden  piles  should  be  used  only  where  they  will  be 
always  wet,  as  they  will  rot  if  alternately  wet  and  dry 
or  if  the  soil  is  not  constantly  water  soaked.  In  this  case 
too,  neighboring  excavation  should  be  anticipated  if  pos- 
sible. Ground  water  level  may  be  lowered  by  drainage 
subsequently  made.  Thus,  in  such  locations  as  New  Or- 
leans, ground  water  level  has  been  lowered  by  the  con- 
struction of  a  sewer  system. 

Concrete  piles,  when  properly  made,  are  more  reliable 
and  durable  than  wooden  piles  and  are  capable  of  tak- 
ing greater  loads.  Fifteen  to  twenty  tons  per  square  foot 
of  sectional  area  may  safely  be  allowed  on  concrete  piles. 
The  higher  unit  loads  are  for  piles  of  larger  diameter,  as 
slender  piles  would  act  as  columns  to  some  extent. 

The  pressure  on  the  footing  for  a  wall  is  found  by  tak- 
ing the  load  per  running  foot  carried  by  that  wall.  This 
includes:  the  weight  of  the  wall  itself,  making  deduc- 
tions for  windows  (say  one-quarter  or  one-third  of  the 
area,  depending  on  the  circumstances;)  the  weight  of  the 
floors  and  roof  bearing  on  the  wall ;  the  live  or  snow  loads 
on  floors  and  roofs  supported  on  the  wall.  From  this  load 
per  running  foot  of  the  wall  and  the  allowed  pressure 
per  square  foot  the  width  of  the  footing  is  determined. 

Footings  under  columns  have  the  load  of  the  column  to 
carry  and  the  load  of  the  footing  itself.  The  area  is  de- 
termined by  the  allowed  pressure  on  the  soil. 


Concrete  walls  and  footings  are  very  much  superior  to 
rubble,  because  the  monolithic  character  enables  the  former 
to  settle  uniformly.  Settlement  in  a  building  is  not  of  seri- 
ous consequence,  except  when  it  is  unequal  settlement,  and 
monolithic  construction  greatly  reduces  the  possibilities  of 
unequal  settlement. 

To  effect  uniform  settlement,  as  stated,  the  unit  pres- 
sure on  the  entire  foundation  should  be  made  as  near  uni- 
form as  possible.  Strictly,  this  cannot  be  done  in  ordi- 
nary cases  because  of  the  unknown  and  varying  amount  of 
the  live  load,  also  because  of  the  fact  that  some  of  the 
walls  or  columns  will  have  a  greater  or  less  proportion  of 
their  load  as  live  load.  Thus,  the  walls  and  exterior  col- 
umns will  have  a  more  steady  load  because  they  take  less 
of  the  floor  load  than  the  interior  columns.  One  way  to 
approximate  equality  of  soil  pressure  is  to  make  the  areas 
of  footings  proportional  to  loads  which  include  one-half 
or  less  of  the  total  live  load  to  be  carried.  This  would 
necessitate  somewhat  greater  area  under  the  parts  tak- 
ing the  smaller  percentage  of  live  load  than  the  allowed 
soil  pressure  for  its  total  load  would  demand. 

When  a  structure  rests  on  piles,  uniformity  of  pressure 
is  effected  by  spacing  the  piles  to  suit  the  intensity  of  the 
load  carried.  For  example,  if  at  one  part  of  a  wall  the 
load  carried  is  four  tons  per  foot  on  piles  that  are  good 
for  12  tons  each,  and  in  another  part  the  load  carried  is 
three  tons  per  foot,  the  spacing  of  piles  should  be  three 
feet  and  four  feet  respectively.  In  large  piers  carrying 
unsymmetrical  loads  the  spacing  of  the  piles  should  be 
such  that  the  center  of  gravity  of  the  piles  will  coincide 
with  the  center  of  gravity  of  the  load. 

For  a  fuller  discussion  of  foundation  methods  and  de- 
signing the  reader  is  referred  to  the  author's  book,  Con- 
crete. 


CHAPTER  II. 

Footings. 

The  footings  of  walls  and  columns  must  of  necessity 
have  greater  area  than  the  walls  and  columns  themselves. 
This  spread  must  be  effected  in  ways  that  will  preserve  the 
structural  strength  and  distribute  the  load  uniformly,  or 
that  will  distribute  the  load  so  that  the  allowed  pressure  on 
the  soil  is  not  exceeded. 

The  simplest  way  to  spread  a  wall  footing  is  to  in- 
crease the  thickness  of  the  wall  by  one  or  more  steps  at 
the  base.  In  a  brick  or  rubble  wall  the  height  of  the  step 
should  be  about  four  times  the  projection  ;  or  if  the  sides 
of  the  wall  slope,  the  spread  on  either  side  should  not  be 
more  than  about  one-quarter  of  the  vertical  height.  The 
same  relation  should  be  observed  in  column  footings  of 
brick  or  rubble. 

In  a  concrete  wall  or  pier  the  projection  or  spread  should 
be  proportioned  according  to  the  allowed  pressure  on  the 
soil  by  the  following  formula : 

sp*=h*  (1) 

where  J  is  the  pressure  in  tons  per  sq.  ft.  allowed  on  the 
soil,  p  is  the  projection  of  the  wall  or  pier  and  h  is  the 
height  in  which  the  step  or  slope  p  occurs. 

For  derivation  of  these  relations,  as  well  as  those  that 
follow,  bearing  on  reinforced  concrete  footings,  see  the 
author's  book  Concrete. 


A  wall  footing  may  be  made  of  reinforced  concrete  as 
shown  in  Fig.  1,  with  the  following  relations: 


fc.35  p  s 
/>=50  d 
.r=9  d 


(2) 
(3) 
(4) 


where  s  is  the  allowed  pressure  on  the  soil  in  tons  per  sq. 
ft,  and  d  is  the  diameter  in  inches  of  square  reinforcing 
rods.  The  projection  p  will  be  found  from  the  load  per 
running  foot  on  the  wall  and  the  allowed  soil  pressure. 
Then  from  equations  (2),  (3),  and  (4)  the  other  dimen- 
sions may  be  found.  Assuming  p=4  ft.  and  s—\l/2  tons, 
h  will  be  2  ft.  \V2  in.  The  reinforcing  rods  would  be  one 
inch  square,  spaced  9  in.  apart. 

This  sort  of  footing  is  appropriate  chiefly  where  the 
soil  is  of  low  bearing  power,  since  the  height  h  required 
for  shear  where  heavy  pressures  are  considered  will  usu- 
ally make  reinforcement  uneconomical,  as  a  somewhat 
greater  height  will  make  reinforcement  unnecessary. 

Any  footings  in  reinforced  concrete  must  be  made  of 
sloppy  concrete,  as  no  other  will  grip  and  protect  the  steel. 
Dry  or  rammed  concrete  is  quite  unsuitable  for  reinforced 
work. 


Fig.  2. 


Column  footings  may  be  made  in  plain  concrete  as  shown 
in  Fig.  2  with  either  stepped  or  sloping  sides.  The  rela- 
tion between  p  and  h  may  be  the  same  as  given  in  Equa- 
tion (1). 


fig.3. 


A  reinforced  concrete  footing  should  be  made  as  shown 
in  Fig.  3.  All  rods  should  pass  under  the  upper  plinth. 
There  are  designs  in  which  the  rods  are  space'  equally 
out  to  the  edges  of  the  rectangle.  This  is  poor  jesign,  as 
the  rods  near  the  outer  edges  can  do  little  or  nothing. 

la  this  footing,  with  s  as  before : 


h=.5 


Equations  (3)  and  (4)   apply  as  in  the  wall  footing. 


(5) 


When  the  outside  line  of  a  wall  is  the  property  line,  of 
course  ill  offsets  must  be  made  on  the  inside.  If  these  off- 
sets are  not  large,  the  pressure  on  the  soil  may  be  con- 
sidered as  uniformly  distributed.  When  the  wall  is  not  a 
long  one,  or  where  there  are  cross  walls,  a  projection  of 
considerable  width  could  be  made  without  the  necessity 
of  assuming  eccentric  load  on  the  foundation. 

If  the  projection  of  a  wall  is  wide  as  in  the  L-shaped 
wall  shown  in  Fig.  5,  unequal  pressure  on  the  soil  must  be 
considered.  The  resultant  pressure  must  fall  within  the 
middle  third  of  the  base.  The  size  and  spacing  of  rods  for 
this  projection,  as  well  as  the  width  and  depth  of  'the  pro- 

9 


Fig.  4. 


Fiq.5. 


Ficj.e. 


jection,  may  be  of  the  same  dimensions  as  those  given 
under  Fig.  1  for  symmetrical  footings.  The  rods  should 
be  given  an  easy  curve  and  not  a  sharp  bend.  The  radius 
of  the  curve  should  be  about  20  times  the  diameter  of  the 
rod.  Rods  should  run  up  into  the  wall  as  indicated  for 
anchorage.  Anchorage  for  a  rod  requires  embedment  in 
concrete  for  a  distance  equal  to  50  times  the  diameter  of 
the  rod. 

The  projection  p  in  the  wall,  shown  in  Fig.  5,  must  be 
less  than  twice  the  thickness  of  the  wall,  that  is,  the  re- 
sultant pressure  must  come  under  the  wall  itself,  so  as  to 
prevent,  or  at  least  minimize,  bending  in  the  wall  itself. 

Wall  footings  are  sometimes  made  by  using  steel  beams 
or  rails  as  needle  beams,  as  indicated  in  Fig.  6.  Rails  are 
not  economical  for  this  purpose,  because  they  are  much 
heavier  for  the  same  strength  than  I-beams. 

The  size  of  I-beams  necessary  for  any  given  case  is 
found  as  follows: 

The  upward  pressure  on  the  soil  is  considered  as  a  uni- 
form load  on  the  beam.  The  beam  is  a  cantilever  with  an 
overhang  or  a  span  /.  This  distance  /  is  a  few  inches  more 
than  the  projection  p,  say  2  to  6  in.,  depending  on  the  mag- 
nitude of  the  footing.  The  load  that  a  beam  can  sustain 
as  a  cantilever  of  a  span  /  is  just  one-quarter  as  much  as 
that  which  it  can  sustain  as  a  simple  beam  of  the  same 
span.  Turning  to  Chapter  VI,  Table  II,  it  is  seen  that 
the  capacity  of  an  I-beam  of  any  span  is  found  by  divid- 
ing the  quantity  Q  in  the  table  by  the  length  of  that  span  in 


10 


feet.  This  capacity  is  in  tons  of  total  load  carried  by  the 
beam  as  a  simple  span.  It  must  be  divided  by  four  to  find 
the  safe  load  that  the  beam  can  take  as  a  cantilever.  If 
the  operation  be  reversed,  we  would  multiply  the  load  on 
the  cantilever  by  four  and  then  by  /  to  find  the  value  of  Q. 
For  example,  if  /  is  four  feet  and  the  upward  pressure  of 
the  soil  is  two  tons  per  sq.  ft.,  we  find  Q  to  be 
4x2x4x4=128.  This  is  the  value  per  running  foot  of  the 
wall.  As  Q,  for  a  10"  I  25  Ib.  is  130,  we  could  use  a 
10"  beam  every  foot. 

These  needle  beams  must  be  completely  surrounded  with 
concrete. 

Grillages  for  column  footings  are  often  made  as  shown 
in  Fig.  7.  In  this  grillage  the  load  of  the  soil  is  first  taken 
by  the  lower  tier  of  beams  to  the  upper  tier;  it  is  then  de- 
livered by  the  upper  tier  to  the  column  base.  The  span 
of  the  lower  tier  is  the  distance  from  the  center  of  outer 
beam  of  the  upper  tier  to  the  edge  of  the  footing.  The 
span  of  the  upper  tier  is  the  distance  from  the  edge  of  the 
footing  to  a  point  a  few  inches  within  the  column  base, 
as  indicated. 


Fig.  7 


$•-* 


1 


C02 


*£& 


Fis 


.8. 


11 


As  an  example,  suppose  it  is  desired  to  proportion  the 
beams  for  a  column  footing  in  which  w  is  10  ft.,  w\  is  8 
ft.,  /  is  3  ft.,  and  /i  is  4  ft,  the  upward  pressure  of  the 
soil  being  4  tons  per  sq.  ft.  The  load  taken  by  the  lower 
tier  of  beams  as  a  cantilever  of  span  /  is  10x3x4=120  tons. 
Multiplying  this  by  4  and  by  the  span  /  we  have  for  the 
aggregate  value  of  Q  for  the  set  of  beams  1,440.  We 
could  use  5-15"  42-lb.  beams,  for  which  Q  is  1,571.  For 
the  upper  tier  of  beams  the  load  carried  is  Wix/i,  as  the 
lower  beams  deliver  this  area  of  load  into  the  upper 
beams.  Q  for  this  set  of  beams  is  then  8x4x4x4x4=2048. 
We  could  use  4-20"  65-lb.  beams,  for  which  Q  is  2,263.6. 

These  beams  would  have  separators  with  bolts'  running 
through  the  set.  Each  would  have  about  three  lines  of 
these  separators. 

Very  often  in  wall  columns  only  one  set  of  beams  will 
be  used  under  the  column  base.  The  size  of  these  will  be 
found  in  the  same  way  as  for  the  grillage  beams. 

Sometimes,  on  account  of  keeping  the  column  footing 
within  property  lines,  two  columns  are  built  on  the  same 
grillage  as  indicated  in  Fig.  8.  Here  the  four  beams  of  the 
upper  tier  take  the  cantilever  load  on  the  area  Wix/i,  and 
are  designed  as  before.  The  lower  beams  carry  the  up- 
ward pressure  on  the  area  tc^x/o,  but  they  act  as  simple 
b^p.'ns  and  not  as  cantilevers.  The  spr.n  is  the  distance 
center  to  center  of  columns,  for  there  is  but  little  balanc- 
ing load  on  the  other  side  of  the  columns.  If  w2  is  6  ft. 
and  lz  is  18  ft,  with  an  upward  pressure  of  the  soil  of  3 
tons  per  sq.  ft.,  Q=18x6x3xl8=5,832.  (Note  that  we  do 
not  multiply  by  4,  as  the  beams  act  as  a  simple  span  and 
not  a  cantilever.)  We  could  use  6-24-in.  80-lb.  beams, 
for  which  Q  is  5,568.  This  is  about  5  per  cent.  shy.  Beams 
weighing  90  Ibs.  per  foot,  would  meet  the  requirements. 

If  either  of  the  columns  of  Fig.  8  carried  a  heavier  load 
than  the  other,  the  beams  could  be  placed  fan-shaped  with 
the  center  of  gravity  of  the  footing  corresponding  with 
•that  of  the  combined  load. 

12 


Fi9 


.9. 


Another  way  to  take  care  of  the  footing  of  a  wall  col- 
umn is  illustrated  in  Fig.  9.  Here  a  lower  tier  of  beams 
is  provided  for  each  column,  but  the  upper  beams  have  the 
added  office  to  perform  of  carrying  the  load  of  the  wall 
column  back  to  the  middle  of  its  grillage.  This  load  is 
carried  on  the  beams  as  a  cantilever  with  an  overhang  I  2. 
The  load  is  the  concentrated  load  of  the  column.  A  beam 
acting  as  a  cantilever  of  a  given  span  supporting  a  load 
at  its  outer  end  will  sustain  only  one-eighth  as  much  total 
load  as  the  same  beam  acting  as  a  simple  span  with  the 
load  uniformly  distributed.  Hence,  to  find  Q,  we  would 
multiply  the  load  by  the  span  and  by  8.  For  example,  sup- 
pose /  2=4  ft.  and  the  column  load  is  70  tons.  Q=70x4x- 
8=2,240.  This  would  require  3-20  in.  80-lb.  beams,  for 
which  Q  is  2,347.2. 

Where  the  depth  permits  of  a  deep  girder  being  used,  a 
plate  girder  or  a  box  girder  is  more  economical  than  beams 
for  heavy  column  loads.  A  column  may  be  riveted  between 
the  webs  of  a  box  girder,  which  acts  as  a  cantilever  to 
carry  tfie  load  to  a  grillage,  located  within  the  property 
line. 


13 


CHAPTER  III. 

Column  Bases. 

Usually  the  foot  of  a  column  rests  on  a  separate  cast 
base.  The  reason  for  this  is  because  the  cast  base  can  be 
set  up  on  the  foundation  and  leveled  and  brought  to  a 
proper  elevation  much  more  easily  than  a  column.  It  can 
also  be  more  readily  located,  as  a  mark  can  be  made  at  the 
center  of  the  base  on  the  planed  top  of  the  same. 

The  cast  base  is  invariably  planed  on  top.  Sometimes 
it  is  also  planed  on  the  bottom ;  but  more  commonly  the 
bottom  is  left  as  cast,  and  the  base  is  set  in  cement  mortar 
or  is  shimmed  up  to  its  proper  level  and  grouted  through 
holes  in  the  bottom. 

In  the  design  of  a  cast  base  the  first  consideration  is  to 
have  area  enough  in  contact  with  the  masonry  so  that  the 
pressure  on  the  same  will  not  be  excessive.  A  pressure  of 
300  Ibs.  per  sq.  in.  may  be  allowed  on  concrete.  This  will 
give  a  basis  for  finding  the  area  of  the  base.  Thus,  a 
load  on  the  column  of  150,000  Ibs.  would  require  a  base  of 
500  sq.  ins.  A  round  cast  iron  column  could  have  a  base 
26  ins.  in  diameter,  or  a  steel  column  could  have  a  square 
base  23  ins.  in  diameter. 


14 


The  usual  design  of  a  base  for  a  cast  iron  column  has  aH 
upper  flange  to  which  the  column  is  bolted  and  a  lower 
plate  resting  on  the  masonry.  This  plate,  as  in  all  other 
masonry  bearing  plates,  should  have  no  unstiffened  pro- 
jection greater  than  about  twice  the  thickness  of  metal  in 
cast  iron  or  four  times  the  thickness  in  steel.  That  is,  p 
in  Fig.  1,  should  not  exceed  2  t. 

When  there  are  stiffening  ribs,  as  in  Fig.  2,  the  spacing 
of  ribs  or  the  thickness  of  the  base  plate  should  be  govern- 
ed by  the  relation  of  ^  to  t.  In  cast  iron  s  should  not  ex- 
ceed about  four  times  t,  and  in  steel  s  should  not  exceed 
about  eight  times  /. 

The  relation  of  a  to  b,  to  give  the  proper  slope 
to  the  rib,  depends  upon  the  thickness  of  rib  and  base  plate. 
If  a  be  made  equal  to  b  in  a  cast-iron  base,  the  stresses  will 
generally  not  be  excessive.  In  a  cast-steel  base  a  may  be 
about  1.5  times  as  great  as  b  without  giving  excessive 
stresses.  Usually,  however,  the  value  of  a  is  made  rela- 
tively less  than  these  ratios  would  show. 

Another  feature  of  a  cast  base  that  should  receive  at- 
tention is  the  location  and  shape  of  the  vertical  webs  under 
the  shaft  of  the  column.  If  the  column  is  of  an  I  shape, 
these  webs  should  be  approximately  the  esame  shape,  as 
shown  in  Fig.  2.  A  column  approximately  square  in  shape 
should  have  the  webs  of  the  base  formed  in  a  square  box. 
It  is  a  good  plan  to  have  a  good  sized  hole  in  the  bottom 
of  this  box  for  grouting  and  a  number  of  other  holes  for 
the  escape  of  air. 

In  large  bases  holes  are  usually  left  for  grouting.  If, 
as  intimated  in  the  last  paragraph,  a  vertical  opening  be 
left  at  the  middle  of  the  base,  this  can  be  filled  with  grout 
to  act  as  a  sink  head  to  give  pressure  to  the  grout.  If  the 
grout  be  allowed  to  rise  in  other  openings  in  the  base,  a 
better  filling  of  the  space  is  assured  than  if  grout  is  poured 
in  several  holes  at  once.  The  latter  method  allows  en- 
trapped air  to  form  pockets  under  the  base. 

Column  bases  in  buildings  are  usually  laid  on  the  con- 
crete footing  without  being  anchored  or  bolted  thereto. 

15 


CHAPTER  IV, 
Columns  and  Other  Compression  Members-. 

Building  columns  may  be  of  wood,  cast  iron,  steel  or  re- 
inforced concrete.  After  the  following  discussion  on  the 
method  of  finding  the  load  carried  by  a  column,  the  meth- 
ods of  designing  the  columns  of  these  several  dasses  will 
be  taken  up. 

The  load  taken  by  a  column  at  any  given  floor  or  roof 
level  would  of  course  be  the  sum  of  the  loads  delivered 
to  it  by  the  beams,  girders  or  trusses  connecting  to  the 
column  at  that  level.  But  to  find  the  reactions  of  all  of 
these  would  generally  be  very  tedious  work.  The  usual 
method  is  to  find  the  area  of  floor  and  the  length  of  wall 
tributary  to  the  column  and  from  suitable  units  for  dead 
and  live  load  to  calculate  the  load  delivered  at  each  floor 
level. 

The  load  per  square  foot  of  the  floor  construction  must 
include  floor  covering,  sleepers,  filling,  arches  or  slabs,  an 
allowance  for  beams,  and  an  allowance  for  girders.  The 
allowance  for  beams  is  a  load  per  sq.  ft.  that  will  c»ver 
the  weight  of  the  beams.  Thus,  if  25-pound  beams  are 
spaced  5  ft.  apart,  this  allowance  is  5  Ibs.  If  girders, 
weighing  45  Ibs.  per  ft,  are  spaced  15  ft.  apart,  3  Ibs.  would 
be  allowed  for  the  girders.  The  area  tributary  to  a  column 
is  the  surface  of  floor  that  the  column  carries.  It  is  usu- 
ally a  rectangle  bounded  by  lines  midway  between  this 
column  and  the  next  in  each  of  the  four  directions  (or 
midway  between  the  column  and  the  wall). 

The  area  for  live  or  superimposed  load  is  the  same  as 
for  dead  load.  Ordinary  partitions  are  usually  considered 
as  covered  by  the  live  load  allowance.  However,  it  is 
well  to  make  an  allowance,  of  say  5  Ibs.  per  sq.  ft.  in  the 
dead  load,  to  cover  the  weight  of  partitions.  Extra  heavy 
partitions  should  be  estimated.  Any  interior  brick  walls 


should  be  allowed  for  by  finding  the  reactions  of  the  beams 
supporting  the  same. 

When  the  walls  are  carried  by  the  columns,  the  full 
weight  of  wall  may  be  estimated  and  the  windows  de- 
ducted; or,  if  the  window  openings  are  fairly  regular,  an 
estimate  may  be  made  of  the  proportion  of  solid  wall,  the 
load  on  the  column  being  calculated  from  this.  Of  course 
each  column  will  tarry  a  length  cvf  wall  equal  to  half  the 
sum  of  the  distances  to  the  next  adjacent  columns,  and  a 
height  equal  to  that  to  the  next  wall  beam  above  or  to  top 
of  wall.  Ordinary  brick  walls  weigh  about  10  Ibs.  per  sq. 
ft.  for  each  inch  in  thickness.  Stone  walls  weigh  about 
12  or  13  Ibs.  per  sq.  ft.  for  each  inch  in  thickness. 

Where  possible,  columns  should  be  symmetrically  loaded, 
as  unsymmetrical  loads  produce  bending  moments  in  the 
column,  and  these  are  seldom  provided  for  in  proportion- 
ing the  section  of  the  column.  In  interior  columns  balance 
of  the  loads  is  usually  easily  accomplished.  In  wall  col- 
umns a  practical  balance  can  be  effected  by  attaching  the 
wall  beams  to  the  outer  side  of  the  column  and  the  floor 
beams  or  girders  to  the  inner  side.  The  most  economical 
and  satisfactory  method  of  offsetting  the  effect  of  a  heavy 
eccentric  load  on  a  column  is  to  make  a  deep  riveted  con- 
nection of  the  girder  to  the  column.  This  puts  the  bend- 
ing stress  into  the  girder  that  would  otherwise  have  to  be 
taken  by  the  column,  and  the  girder  is  generally  amply 
able  to  carry  the  bending  stress.  The  riveted  connection 
may  be  for  the  full  depth  of  the  girder,  or  it  may  be  made 
greater  than  the  depth  by  use  of  gusset  plates  or  corner 
brackets.  In  a  rolled  beam -top  and  bottom  riveted  flange 
connections  aid  greatly  in  overcoming  bending  due  to  ec- 
centric loads. 

Wooden  Columns,  The  allowed  load,  in  direct  compres- 
sion on  a  wooden  column  is  very  simply  found.  It  depends 
upon  the  ratio  of  the  free  height  of  the  column  to  the  least 
width  "This  raticT'bf  free'  or  unsupported  height  to  width 
must  b^'' clearly  undfe^tood,  however.  In  a  simple  post 
without*  traces  from  tee  to  top  thetfree  height  is  the  full 


length  of  the  post.  In  posts  having  knee  braces  or  struts 
connecting  to  some  part  of  the  building  capable  of  offer- 
ing ample  resistance,  the  free  height  is  the  distance  from 
the  base  to  the  point  where  the  braces  connect. 


If  the  braces  hold  the  column,  in  only  one  direction,  as  in 
Fig.  1,  there  will  be  two  ratios  to  consider,  namely:  l/d 
and  I' /d' .  The  smaller  of  these  two  ratios  will  be  the 
governing  factor  in  determining  the  strength  of  the  col- 
umn. It  is  to  be  observed  that  the  braces  must  be  capable 
of  holding  the  column  in  line.  Two  equally  strong  or 
equally  weak  columns  braced  together  by  a  horizontal  brace 
would  not  be  shortened  in  their  effective  length  by  such  a 
brace. 

When  the  ratio  of  length  to  width  of  a  wooden  column 
is  known  the  allowed  load  per  square  inch  is  as  follows : 

For  yellow  pine  or  oak 1,000—18  l/d 

For  white  pine 800—15  l/d 

In  the  following  table  the  allowed  load  per  sq.  in.  is 
shown  for  three  different  ratios. 

TABLE  I. 

STRESSES  PER  SQ.  IN.   ALLOWED  ON  WOODEN  POSTS. 

Yellow,Pine  or 


Ratio 

White  Oak 

White  Pine 

30 

460 

350 

20 

640 

500 

10 

820 

650 

18 


For  example,  suppose  an  8x8  yellow  pine  post  is  10  feet 
long.  The  length  is  15  times  the  width  and  the  unit  com- 
pression allowed  is  730  Ibs.  per  sq.  in.  This  post  would 
carry  safely  730x64=46,720  Ibs.  A  white  pine  post  6x8  in 
section  and  eight  feet  long  would  have  a  ratio  of  length  to 
least  width  of  16.  A  load  of  560  Ibs.  per  sq.  in.  could 
be  allowed,  or  a  total  load  of  26,880  Ibs. 

Generally,  wooden  posts  should  not  be  less  in  width  than 
Ir30  of  the  length. 

The  base  of  a  wooden  post  or  column  is  sometimes  made 
of  cast  iron.  A  socket  is  cast  in  the  base  into  which  the 
post  fits.  The  spread  of  this  cast  base  must  be  such  as 
to  keep  the  pressure  on  the  masonry  within  the  allowed 
limits.  Thus,  the  8x8  post  of  the  last  paragraph  with  its 
load  of  46,720  Ibs.,  if  250  Ibs.  per  sq.  in.  be  allowed  on  the 
masonry,  would  require  -37  sq.  in.  of  base.  A  base  14 
ins.  sq.  would  do  for  this  column.  As  the  projection 
around  the  column  is  3  ins.  the  thickness  should  be  half  of 
this  or  \l/2  in. 

Cast-iron  caps  are  very  often  used  at  the  tops  of  col- 
umns to  act  as  splices  and  as  seats  for  girders.  Steel 
plates  or  angles  would  be  very  much  better,  as  cast  iron  is 
brittle  and  liable  to  be  broken  by  the  concentration  of  the 
beam  load  on  the  edge  of  the  bracket.  Fig.  2  shows 
a  suggested  detail. 


Fia.  2 


19 


Cast-iron  Columns.  The  allowed  load  in  direct  com- 
pression on  a  cast-iron  column  is  found  in  a  similar  man- 
ner to  that  on  a  wooden  column.  It  is  true  that  there  are 
many  formulas  for  the  strength  of  a  cast-iron  column,  but 
they  are  for  the  most  part  highly  theoretical  and  their  al- 
lowed unit  loads  are  not  borne  out  by  tests.  A  few  simple 
rules  for  designing  and  a  simple  formula  for  the  allowed 
compression  are  all  that  a  material  such  as  cast  iron  de- 
mands. 


Fig.  3  shows  the  common  sections  used  in  cast-iron  col' 
umns.  The  round  and  square  shapes  are  generally  used 
for  interior  or  exposed  columns.  The  oblong  column  may 
be  used  in  a  wall  or  between  windows.  The  H-shaped 
column  may  also  be  used  between  windows. 

The  thickness  t  should  ordinarily  be  not  less  than  about 
Y2  in.  In  the  H-shaped  column  the  thickness  /  should  not 
be  less  than  about  one-fifth  of  x. 

The  allowed  unit  stress  on  cast-iron  columns  should  not 
exceed 

7,600-40  l/d 

where  /  is  the  unsupported  length  of  the  column  and  d  is 
the  least  width.  In  Fig.  3,  d  is  indicated.  It  will  be  the 
outside  diameter  of  a  round  or  square  column.  In  the 
other  shapes  it  will  be  di  or  d2,  depending  upon  the  un- 
supported length  of  the  column  for  these  two  directions. 
If  the  column  is  supported  in  one  direction  and  not  sup- 
ported in  the  other,  there  will  be  two  ratios  to  consider, 
namely:  h/di  and  h/dz;  /,  being  the  free  length  cor- 
responding to  di,  etc.  The  smaller  of  these  two  ratios 
will  determine  the  unit  load  to  use  on  the  column. 

20 


From  the  foregoing  unit  stress  the  allowed  load  per  sq. 
in.  on  cast-iron  columns  may  be  found  for  various  ratios 
and  tabulated  as  follows: 

TABLE  IT. 

STRESSES    PER    SQ.    IN.     ALLOWED    ON    CAST-IRON    POSTS. 


Ratio       Allowed  Stress     Ratio     Allowed  Stress 

40 
30 

6000 
6400 

20 
10 

6800 
7200 

Generally,  cast-iron  columns  should  not  be  less  in  width 
than  1-40  of  the  length. 

For  convenience  in  finding  the  areas  of  hollow  square 
and  circular  columns,  the  following  table  is  given.  The 
column  area  will  of  course  be  the  difference  between  the 
inner  and  the  outer  circle  or  square.  When  the  outside  di- 
ameter and  the  desired  area  are  known,  the  area  of  the 
inner  circle  or  square  will  be  the  difference  between  that 
of  the  outer  circle  or  square  and  the  required  area.  From 
this  the  inner  diameter  can  be  found  in  the  table. 


TABLE  III. 


Areas  of  Squares  and  Circles, 


Area 

Area 

Area 

Area 

| 

Area 

Area 

_ 

Dia.  |Ro'nd  |Sq'art 

Dia.  |  Round 

|  Square 

Dia.  |  Round 

Square 

3 

7.069|   9.000 

7 

38.485 

49.000 

11      1 

95.0331121.000 

8.296 

10.563 

41.283 

52.563 

11J4J   99.402J126.563 

3l/2 

9.621 

12.250 

71/* 

44.179|    56.250 

11/4 

132.250 

324 

11.  045|  14.  063 

734 

47.1731    60.063 

1134|108.434 

138.063 

4 

12.566  16.000 

8 

50.2661    64.000 

12      1113.097 

144.000 

4% 

14.186  18.063 

8/4 

53.4561   68.063 

12i4|117.859 

150.063 

4*/2 

15.904|20.250 

Sl/2 

56.745|    72.250 

12J4  122.718 

156.250 

17.721|22.563 

834 

60.1321    76.563 

1234)127.676 

162.563 

5  4 

19.635125.000 

9 

63.617     81.000 

13      |132.  732|169.  000 

5J4i21.648i27.563 

9J4 

67.201  1    85.563 

13J4I137.886J175.563 

5^123.758 

30.250 

9/2 

70.8821   90.250 

1354  143439  182.250 

524 

25.967 

[33.063 

74.662 

95.063 

1334  |148.489|  189.  063 

6 

28.274 

36.000 

10     I    78.540  1  100.  000 

14 

153.9381  196.000 

6J4i30.680i  39.063 

10J4I   82.516|105.063 

14/4 

159.4851203.063 

6^|33.183|42.250 

lO^j    86.590illO.250 

14J4|165.  1301210.250 

634135.785145.563 

10341    90.7631115.563 

14341170.8731217.563 

Cast-iron  columns  are  not  to  be  recommended  for  build- 
ings of  mere  than  about  three  or  four  stories  in  height. 
They  should  not  be  used  in  any  case  in  a  building  whose 
lateral  stability  depends  in  any  wise  on  the  columns,  such 
as  one  whose  exterior  walls  are  carried  by  the  metal 
frame.  Cast  iron  lacks  toughness  and  should  be  used  only 
in  simple  compression  in  columns  and  in  situations  where 
there  is  little  or  no  bending  stress. 

Given  an  example  where  the  wall  between  two  buildings 
is  to  be  removed  and  replaced  by  cast-iron  columns.  As- 
sume the  width  of  each  building  to  be  20  feet;  the  height 
of  the  first  story  14  ft.;  three  stories  above  this  of  11  ft. 
each;,  thickness  of  wall  13  in.;  total  weight  for  floors  150 
Ibs.  per  sq.  ft. ;  total  weight  for  roof  120  Ibs.  per  sq.  ft. ; 
spacing  of  columns  18  ft. 

Each  column  will  carry  the  following  load: 

18  ft.  of  wall,  33  ft.  high =18x33x130=  77,220 

20x18  ft.  of  roof,  at  120 =20x18x120=  43,200 

3  floors,  360  sq.  ft.  each,  at  150 =3x360x150=162,000 


282,420 

Assume  a  round  section  of  column  12  ins.  in  outside  di- 
ameter. The  ratio  l/r  is  14/1  or  14.  The  allowed  load  per 
sq.  in.  is  7,040  Ibs.  The  area  required  is  40  sq.  ins.  A 
circle  12  ins.  in  diameter  has  an  area  of  113  sq.  ins.  This 
leaves  73  sq.  ins.  as  the  area  of  the  inner  circle,  or  say 
a  9.5-in.  circle.  This  gives  a  thickness  of  metal  of  \l/4  in. 

At  the  top  of  this  column  there  will,  of  course,  be  pairs 
of  I  beams  or  a  box  girder  to  carry  the  load  of  the  wall 
and  the  floors  above.  These  beams  would  not  have  to  be 
designed  to  carry  all  of  this  load  as  uniformly  distributed, 
because  the  rigidity  of  the  solid  wall  wo'jld  allow  much 
of  it  to  be  carried  by  the  wall  directly  to  the  columns.  Of 
the  141  tons  on  a  pair  of  beams  of  a  span  of  18  ft,  we 
may  assume  100  tons  as  a  uniform  load  on  a  pair  of  beams. 
The  value  of  Q  in  the  table  of  the  capacity  of  beams  is 


then    100x18=1,800.     Two   24-in.   80-lb.   beams   would   bo 
used.    These  have  a  combined  value  of  Q  equal  to  1,856. 

The  base  of  this  column  should  not  be  made  to  rest  di- 
rectly on  the  foundation  wall,  but  should  have  distributing 
beams  so  that  the  pressure  on  the  wall  will  not  be  exces- 
sive. If  two  beams  be  used,  each  10  ft.  in  length,  the  load 
per  foot  on  the  pair  of  beams  will  be  141-f-10  or  14.1  tons 
per  ft.  The  beams  will  have  a  cantilever  span  of  about 
4.5  ft.  Each  I  beam  will  have  a  load  on  this  cantilever  of 
7.05x4.5=31.7  tons.  For  the  value  Q  of  the  table  this  is  to 
be  multiplied  by  4  and  by  the  span  4.5,  or  Q =3 1.7x4x4. 5- 
=571.  There  will  then  be  required  2-15"  80-lb.  beams. 

The  area  of  the  flanges  of  these  beams  in  bearing  on 
the  wall  is  2x6.4x120=1,536  sq.  ins.  This  is  a  pressure  on 
the  wall  of  282,420^-1,536=184  Ibs.  per  sq.  in.  The  wall 
should  have  a  concrete  or  a  cement  mortar  finish  in  which 
to  bed  the  beams. 


Fig. -4-. 

Splices.  Cast-iron  columns  are  generally  spliced  by  four 
or  more  bolts  through  flanges.  The  flanges  are  made  of 
about  the  same  thickness  as  the  shell  of  the  column.  The 
splice  is  made  about  at  the  floor  level.  The  flanges  should 
be  about  2l/2  or  3  inches  wide  to  allow  space  for  bolt  heads. 
The  bolr.  holes  should  be  drilled  and  not  cored.  The  enda 
of  columns  should,  of  course,  be  planed  true. 

Where  a  change  in  section  of  cast-iron  columns  occurs, 
provision  must  be  made  for  carrying  the  load  from  the  up- 
per to  the  lower  section.  This  may  be  done,  as  in  Fig.  5, 
by  making  extra  heavy  flanges,  stiffened  with  ribs,  on  the 
upper  column. 


Generally,  the  shaft  of  a  cast-iron  colunm,  should  be  uni- 
form from  end  to  end  of  the  column.  If  the  column  is 
flared  out  for  an  ornamental  head  or  base,  it  should  be 
strengthened  by  inside  ribs  to  carry  the  column  load. 


Ficj.8 

Beams  generally  connect  to  cast-iron  columns  by  means 
of  brackets  on  which  they  rest  and  lugs  for  bolted  con- 
nection to  the  web.  The  brackets  are  usually  made  as 
indicated  in  Figs.  6,  7,  8.  These  brackets  should  project 
about  3  or  4  ins.  from  the  face  of  the  column.  There  is 
no  advantage  in  a  wide  shelf,  but  rather  the  reverse,  as  the 
beam  is  apt  to  bear  on  the  outer  edge  and  produce  heavy 
bending  stresses  on  the  bracket.  There  should  be  a  sti-ffen- 
ing  rib  under  each  -beam,  not  less  than  twice  as  deep  as 
the  width  of  the  bracket.  The  shelves  and  ribs  should 
have  a  thickness  of  metal  about  equal  to  that  of  the  shell 
of  the  column,  but  not  less,  for  ordinary  work,  than  about 
one  .inch.  The  shelves  are  not  planed,  but  are  cast  smooth; 
the  bolt  holes  are  usually  cored. 


Eccentric  of  unbalanced  loads  should  be  guarded  against 
in  cast-iron  columns,  because  of  the  lack  of  toughness  in 
the  metal. 

Steel  Columns.  There  are  many  forms  of  steel  columns 
from  the  single  angle  up  to  the  built  column  of  several 
hundred  square  inches  of  sectional  area.  The  selection 
of  an  appropriate  style  of  column  for  any  given  case  will 
depend  upon  the  several  conditions  of  the  case. 

There  are  many  column  formulas  that  purport  to  give 
the  correct  load  that  will  cause  ultimate  failure  in  a  col- 
umn or  the  correct  safe  load;  but,  excepting  the  formulas 
of  the  form  known  as  the  Euler  formula,  these  usually 
bring  in  empirical  "constants"  that  are,  in  fact,  not 
constant  and  that  depend  upon  conditions  that  cannot  be 
made  uniform  in  commercial  work. 

A  steel  column  acts  partly  as  a  spring  to  resist  bowing 
and  partly  as  a  shaft  in  compression  to  resist  crushing. 
The  ultimate  strength  of  a  slender  column  can  be  calcu- 
lated closely,  but  the  ultimate  strength  of  a  shorter  column 
can  only  be  very  roughly  approximated.  The  ratio  of 
slenderness  of  a  column  is  the  ratio  between  the  length  and 
the  least  radius  of  gyration  of  the  cross  section.  The  large 
majority  of  compression  members  have  ratios  of  slender- 
ness  varying  between  30  and  150,  and  it  is  between  these 
limits  that  the  greatest  uncertainty  as  to  calculated  strength 
exists.  When  a  compression  member  is  very  short,  its 
ultimate  unit  strength  is  nearly  equal  to  the  ultimate  unit 
strength  of  cubical  specimens;  when  the  member  has  a 
ratio  of  slenderness  of  150  or  more,  its  ultimate  strength 
is  the  definite  value  shown  by  the  Euler  formula. 

A  few  words  are  deemed  advisable  here  in  the  way  of 
warning  to  the  inexperienced  designer.  It  is  often  asked, 
"What  is  the  factor  of  safety  of  a  certain  structure?"  and 
thf  answer  usually  given  is  4  or  5,  according  as  the  de- 
signer thinks  he  has  split  up  the  ultimate  strength  of  his 
members  into  4  or  5  parts.  The  builder  may  say  that  he 
is  satisfied  with  a  factor  of  safety  of  3  or  less,  and  the  de- 
signer is  asked  to  cut  down  his  sections  accordingly.  This 

25 


is  a  dangerous  undertaking,  especially  when  the  commonly 
used  column  formulas  are  taken  at  their  face  value.  As 
the  author  has  shown  in.  Railway  Age-Gazette,  July  2,  1909, 
the  Gordon-Rankine  column  formula  shows  apparent  ulti- 
mate strengths  of  columns  that  are  in  some  cases  more  than 
100  per  cent  'too  great.  This  subject  is  more  fully  treated 
in  the  author's  Structural  Engineering,  Book  III. 

In  some  manufacturers'  handbooks  the  supposed  ultimate 
strength  of  columns  is  worked   out  on  the  basis  of  the 
Gordon-Rankine  formula  for  values  of  the  ratio 
Length    in    feet 


Radius   of  gyration   in  inches 

as  high  as  20  or  more.  This  is  an  actual  ratio  of  slender- 
ness  of  240.  It  is  entirely  too  slender  for  a  practical 
column.  Furthermore,  the  ultimate  strength  given  for  a 
pin-ended  column  of  this  ratio,  is  nearly  12,000  Ibs.  per 
sq.  in.  The  actual  ultimate  strength  of  this  column  is 
5,000  Ibs.  per  sq.  in.,  even  if  the  column  be  made  of  the 
highest  grade  and  hardest  steel  that  it  is  possible  to  manu- 
facture. 

Designers  are  warned  against  using  columns  or  other 
compression  members  of  a  ratio  of  slenderness  greater 
than  about  T50.  Some  specifications  and  building  codes  do 
not  allow  a  greater  ratio  than  120. 

What  is  known  as  the  straight-line  formula  for  the 
strength  of  a  column  is  better  than  formulas  of  the  Gor- 
don-Rankine type,  because  the  straight-line  formula  shows 
very  low  strength  for  slender  columns  and  because  it  agrees 
more  nearly  with  tests. 

A  straight-line  formula  in  common  use  for  building 
work  gives  a  unit  stress  per  sq.  in.  equal  to 

15,200—58  l/r. 

where  /  is  the  length  in  inches  and  r  is  the  least  radius  of 
gyration  in  inches.  In  a  well-built  and  properly  designed 
and  centrally-loaded  column,  this  formula  gives  the  load 
that  can  safely  be  sustained.  The  factor  of  safety  is  a 
matter  depending  entirely  on  the  perfection  of  the  work 

26 


and  is   a  value  quite  impossible  to   determine.     Designers 
are  cautioned  to  adhere  to  the  -formula. 

The  length  /  in  the  column  formula  is,  of  course,  the 
unsupported  or  unbraced  length  of  the  column  or  other 
compression  member.  As  explained  heretofore  in  this 
chapter,  there  may  be  two  or  more  ratios  of  slenderness 
to  consider.  A  compression  member  may  be  braced  in 
one  direction  and  free  to  buckle  or  bow  in  another  direc- 
tion. Steel  compression  members  may  be  of  unsym- 
metrical  sections,  as  in  the  case  of  a  single  angle  or  zee 
bar;  in  such  case  the  diagonal  radius  of  gyration  must  be 
found,  as  this  is  less  than  the  radii  on  the  rectangular 
axes.  A  single  angle  or  zee  bar  would  fail  by  bowing  in  a 
diagonal  direction. 

Single  channels  and  single  I-beams  do  not  make  good 
compression  members,  because  the  radius  of  gyration  with 
the  neutral  axis  parallel  with  the  web  is  so  small.  In  gen- 
eral, these  should  not  be  used  as  compression  members,  un- 
less they  are  braced  at  close  intervals,  or  bolted  to  a  wall, 
or  built  into  a  wall. 

Tables  IV  to  XX  give  the  total  load  allowed  on  com- 
pression members  of  various  shapes.  These  tables  should 
be  used  with  caution  and  a  knowledge  of  their  limitations. 
Correct  design  and  proper  end  details  of  columns  are  es- 
sential to  produce  a  column  that  will  have  safe  carry- 
ing capacities  as  shown  in  the  tables. 

The  heavy  zig-zag  lines  in  the  several  tables  show  the 
limits  of  safe  length  of  columns  at  about  120  times  the 
radius  of  gyration.  Preferably  the  length  of  column  should 
be  kept  within  this  limit.  In  some  cases  the  ratio  may  be 
made  as  high  as  150,  when  values  to  the  right  of  the  zig- 
zag line  apply.  The  value  of  the  radius  of  gyration  of 
nearly  all  of  these  sections  may  be  found  in  Godfrey's 
lables.  The  following  rules  apply  approximately  for  some 
of  the  sections : 

For  the  star-shaped  sections  shown  in  Table  IX,  the 
value  of  r  is  about  four-tenths  of  the  width  of  the  leg  of 

27 


•ne  angle.  The  limit  of  120  times  r  is  then  about  48  times 
the  width  of  the  leg  of  one  angle.  Thus,  for  4 — 4"X4" 
angles  this  limiting  length  would  be  16  ft. 

For  gas  pipe  the  radius  of  gyration  is  about  .35  of  the 
outside  diameter.  At  120  radii  the  unsupported  length  is 
then  about  40  times  the  outside  diameter., 

For  Bethlehem  H  Sections  the  radius  of  gyration  is 
about  .4  of  the  width  B  of  flange,  hence  120  radii  is  about 
48  times  the  flange  width. 

For  the  sections  shown  in  Tables  XII  and  XIII  r  is  about 
.20  to  .22  times  the  width  of  flange,  hence  120  radii  is  about 
25  times  the  flange  width. 

For  the  channel  columns  of  Table  XVI  r  is  about  .4  of 
the  depth  of  channel,  hence  120  radii  is  about  48  times 
the  depth  of  channel. 

For  the  zee-bar  columns  r  (minimum  value)  is  about  .62 
times  the  web  of  one  zee  bar.  The  limit  of  column 
length,  at  120  radii,  is  18.5  ft.  for  3-in.  zees,  24.5  ft.  for 
4-in.  zees,  31  ft.  for  5-in.  zees,  and  37  ft.  for  6-in.  zees. 

Tables  IV  and  V  give  the  strength  of  single  angles  in 
compression,  but  in  order  to  develop  the  strength  shown 
in  these  tables  the  angles  should  preferably  be  milled  on 
the  ends.  They  need  a  square  end  bearing,  so  that  the 
load  will  not  be  eccentric.  Connection  by  means  of  rivets 
through  each  leg  of  the  angle  may  be  sufficient  to  balance 
the  load,  but  that  connection  should  be  to  rigidly  held  parts. 
Single  angles  should  generally  be  avoided  as  members  of 
a  truss,  but  if  used,  the  allowed  stress  should  be  only 
about  half  of  that  shown  in  the  table,  so  as  to  allow  for 
eccentricity.  This  is  true,  whether  or  not  both  legs  of 
the  rngle  are  connected  with  rivets  at  the  ends.  When 
the  stress  is  applied  to  the  end  of  an  angle  by  a  gusset 
plate,  extra  lug  angles  connecting  to  the  outstanding 
flange  do  not  centralize  the  stress  from  the  gusset  plate. 

When  a  single  angle  used  as  a  post  has  a  channel  riveted 
to  each  flange,  as  in  Fig.  10,  a  good  rigid  end  connection 
is  obtained,  and,  if  the  base  of  the  post  is  milled  and,  has 
a  sguare  bearing,  the  post  may  be  taken  as  -good  for  the 

28 


value  in  the  table.  If  the  angle  is  not  milled  on  the  end» 
its  value  in  compression  may  be  determined  by  the  rivets 
in  the  lugs  at  the  end.  Very  frequently  these  angles  are 
simply  sheared  off  at  the  ends  and  do  not  bear  against 
the  base  plate. 

Figs.  9,  10  and  11  illustrate  small  angle  posts.  When 
two  angles  are  used  as  a  post  or  compression  member,  they 
should  be  riveted  together  at  intervals  of  a  foot  or  two,  so 
that  they  will  act  together  as  one  member.  When  they 
are  separated,  as  in  a  truss  by  the  thickness  of  a  gusset 
plate,  washers  are  used  between  the  angles  at  these  rivets. 


Fig.  9. 


Bit 

Fig.lO. 


o;;;o 


Fig.  II. 


Compression  members  are  sometimes  made  of  twd  an- 
gles separated  several  inches  and  joined  by  small  batten 
plates  at  intervals  of  three  or  four  feet.  These  do  not 
make  good  compression  members,  unless  they  are  consid- 
ered as  two  separate  angles,  and  the  ratio  of  slenderness 
so  taken.  When  the  two  angles  are  joined  by  lattice  from 
end  to  end  of  member,  they  may  be  considered  as,  one 
member,  for  then  the  triangular  system  of  lattice  bars 
compels  one  angle  to  aid  the  other  in  resisting  buckling 
from  end  to  end  of  the  member. 

Gas  pipe  posts  usually  have  a  threaded  cast  iron  flange 
for  an  end  connection. 


Beam  connections  to  steel  columns  and  column  splices 
will  be  considered  in  another  chapter. 


In  selecting  the  sections  for  columns  in  the  successive 
stories  of  a  building,  they  should  be  arranged  so  that  the 
metal  of  the  upper  section  will  bear  against  metal  of  the 
lower  section,  unless  special  provision  is  made  in  the  splice. 
Frequent  changes  in  the  general  outside  dimensions  of  the 
columns  should  not  be  made,  as  these  involve  special 
splices  and  more  irregular  beam  connections.  In  closed 
channel  sections  the  thickness  of  cover  plates  and  the 
weights  of  channels  may  be  reduced,  using  the  same  depth 
of  channel  for  several  tiers.  In  I-shaped  built  columns  cover 
plates  may  be  reduced  in  number  and  thickness,  in  the 
successive  tiers,  then  omitted ;  then  angles  may  be  reduced 
in  thickness  and  in  length  of  legs,  maintaining  the  same 
web  plate  or  distance  back  to  back  of  angles.  (The  distance 
back  to  back  of  angles  is  usually  made  Y-Z  inch  greater 
than  the  width  of  web  plate.) 

Reinforced  Concrete   Columns. 

True  reinforced  concrete  must  of  necessity  be  concrete 
reinforced  or  strengthened  where  the  concrete  is  weak. 
Any  system  that  combines  steel  and  concrete  where  the 
steel  is  in  compression  is  not  reinforced  concrete,  but  may 
be  termed  concrete-steel,  a  combination  of  the  two  ma- 
terials assumed  to  be  acting  together.  Concrete  is  strong 
in  compression  (confined  or  in  short  blocks),  but  weak  in 
tension  and  shear.  If  steel  is  to  reinforce  concrete,  it  must 
do  it  by  making  up  the  lack  existing  in  the  concrete,  that 
is,  it  must  take  up  the  tensile  stresses  and  relieve  the  con- 
crete of  the  same.  There  are  tensile  stresses  in  concrete 
acting  as  a  simple  post  or  column.  This  is  scarcely  recog- 
nized in  books  on  engineering,  though  it  is  of  tremendous 
importance,  especially  in  reinforced  concrete  design.  The 
cement  mortar  that  is  strongest  in  tension  will  make  the 
strongest  column.  A  bundle  of  thin  straight  wires  would 
be  useless  as  a  column.  But  if  the  same  wires  were  tight- 
ly bound  about  with  a  spiral  wire,  a  heavy  load  could  be 
borne  by  the  same  thin  wires.  Slender  rods  in  a  concrete 
shaft  are  very  imperfectly  and  insecurely  held  together 


and  held  from  buckling  by  the  concrete.  Hence  a  con- 
crete column  built  with  slender  rods  in  it,  with  the  idea 
that  these  rods  will  reinforce  it,  is  most  absurdly  de- 
signed. In  spite  of  the  fact  that  such  design  is  standard 
and  accepted  by  nearly  all  authorities  on  reinforced  con- 
crete, it  is  absolutely  dangerous  and  indefensible.  It  has 
been  the  cause  of  a  large  number  of  very  disastrous 
wrecks.  Such  design  and  practice  cannot  be  too  severely 
condemned.  Books  on  reinforced  concrete  are  woefully 
lacking  and  inexcusably  blameworthy  in  this  respect — that 
they  encourage  and  hold  out  as  standard  and  proper  de- 
sign such  miserably  poor  construction.  For  a  full  pre- 
sentation of  this  subject  the  reader  is  referred  to  the  au- 
thor's book  "Concrete,"  to  his  paper,  read,  before  the 
American  Society  of  Civil  Engineers  in  March,  1910,  en- 
titled, "Some  Mooted  Questions  in  Reinforced  Concrete 
Design,"  and  to  files  of  Engineering  News  and  Concrete 
Engineering,  1907  to  1910,  inclusive.  No  valid  argument 
has  been  brought  forth  to  controvert  the  author's  posi- 
tion ;  tests  and  wrecks  have  amply  demonstrated  the  sound- 
ness of  it. 

In  this  book  only  one  form  of  reinforced  concrete  col- 
umn will  be  considered  as  worthy  of  use,  namely,  the 
hooped  column.  A  discussion  of  the  proper  dimensions 
of  such  a  column  will  be  found  in  the  author's  book,  "Con- 
crete." These  are  as  follows : 

Reinforced  columns  will  be  round  or  octagonal.  They 
will  have  embedded  in  the  concrete  a  coil  of  square  steel 
having  a  diameter  one-fortieth  of  the  diameter  of  the  col- 
umn and  eight  upright  rods  just  inside  the  coil  and  wired 
to  the  same,  so  as  to  prevent  displacement  of  both  coil 
and  straight  rods.  The  coil  will  have  a  diameter  seven- 
eighths  of  that  of  the  column  and  a  pitch  one-eighth  of 
the  diameter  of  the  column.  The  upright  rods  will  be 
of  the  same  section  as  the  rod  in  the  coil.  Where  a  coil 
ends,  the  next  coil  will  lap  one-half  of  a  circle.  Where 
upright  rods  end  there  will  be  a  lap  of  50  diameters  of 
the  steel  rods. 

31 


On  a  column  such  as  that  described  in  the  last  para- 
graph a  load  per  square  inch  may  be  allowed  on  the  full 
section  of  the  concrete,  of  550  pounds,  on  columns  having 
a  length  not  more -than  ten  times  their  diameter.  Between 
10  and  25  diameters  the  following  load  will  be  allowed : 

p  =670— 12  l/D 

where  p  =load  per  square  inch, 
/  =length  in  inches, 
D=diameter  in  inches. 

Reinforced  concrete  columns  should  not  be  of  greater 
length  than  25  times  their  diameter. 

Reinforced  concrete  cannot  be  recommended  for  eco- 
nomic construction  in  columns.  Also  the  difficulties  in 
the  way  of  complete  filling  of  the  forms  are  many.  Bet- 
ter construction  is  effected  by  the  use  of  steel  columns 
surrounded  with  concrete  for  fire  protection  or  concrete 
columns  in  which  are  embedded  stiff  steel  sections,  which 
depend  in  a  small  degree  only  upon  aid  supplied  by  the 
concrete.  These  two  classes  of  columns  will  be  more 
fully  described  in  what  follows. 

When  steel  columns  are  surrounded  by  concrete,  to  a 
depth  of  say  \l/t  or  2  inches  over  the  metal,  the  steel 
columns  should  be  designed  in  every  respect  as  columns 
quite  free  of  concrete,  or  as  those  protected  by  tile. 

Efficient  and  safe  columns  can  be  made  of  steel  angles 
or  other  stiff  steel  sections  held  together  at  intervals  by 
batten  plates  riveted  thereto,  the  whole  being  surrounded 
and  filled  with  concrete.  These  batten  plates  should  be 
sufficiently  close  so  that  each  individual  angle,  or  other 
stiff  section  of  which  the  steel  column  is  composed,  will 
act  as  a  short  column  between  the  batten  plates.  Such 
a  steel  column  would  not  make  a  good  compression  mem- 
ber alone,  but  the  concrete  can  be  relied  upon  to  add  suf- 
ficient stiffness  to  the  columns,  within  certain  limits.  In- 
stead of  battens,  lattice  may  be  used  in  the  columns,  ex- 
cept at  girder  connections,  where  angle  shelves  may  b( 
used  upon  which  to  rest  the  girders.  The  columns  maj 
be  left  open  at  girders  for  the  passage  of  continuou; 
'rods. 

32 


It  is  recommended  that  concrete-steel  columns  such  as 
those  described  in  the  preceeding  paragraph  be  propor- 
tioned on  the  basis  of  a  flat  unit  stress  of  16,000  Ibs.  per 
sq.  in.,  and  that  the  width  out  to  out  of  steel  column  be 
not  less  than  one-twelfth  of  the  unsupported  height,  and 
that  concrete  to  a  depth  of  2  inches  be  used  outside  of 
all  metal.  The  concrete  should  be  considered  merely  as 
protecting  the  steel  and  carrying  shear  from  one  side  to 
the  other  of  the  column.  No  compressive  value  should 
be  allowed  for  the  concrete. 


Pig.  1 2.. 


Fig.!3. 


Fig.14.         Fig.15. 


Figs.  12  to  15,  inclusive,  show  examples  of  these  con- 
crete-steel columns.  The  dotted  lines  indicate  batten  plates 
or  lattice  bars.  A  good  rule  for  the  spacing  of  batten 
plates  is  to  make  them  no  farther  apart  than  twelve  times 
the  width  of  the  flange  of  the  angle  or  channel. 


TABLE   IV. 

Total  Load  in  Thousands  of  Pounds, 
Allowed  on  Single  Angles  as  Com- 
pression Members. 

Size  of                       Unsupported    Length    of    Member. 

Angle.       |    2  ft. 

3ft. 

4  ft.        5  ft.        6  ft.        7  ft. 

8ft. 

2     x2     xy4 
2     x2     xy& 

2y2x2y2xy4 
2y2x2y2xy2 

3     x3     xy4 
3     x3     xH 

3y2x3y2*y& 

3y2x3y2x}/4 
2y2x2     xV4 

2y2x2   Xy2 
3   x2y2xy4 
3    x2y2*y2 
3?4x2j4xj4 
3y2x2y2xy8 

3y2x3     xfg 
3^x3     xft 
4     x3     xH 

4     x3     xM 

11 

16 
15 
28 
18 
43 
33 
62 
13 
24 
16 
31 
18 
42 
30 
56 
32 
61 

9 
13 
13 

24 
17 
39 
30 
57 
11 
20 
15 
28 
16 
38 
27 
51 
30 
56 

8 
11 

11 
21 
15 
35 
28 
52 
9 
17 
13 
25 
14 
33 
25 
46 
27 
51 

6 
9 

8 

15 

10 
22 
"20~ 

ii 

14 
27 
16 
31 

10 
18 
13 
31 
25 
47 

27 
23 

42 

7 

14 

10 
18 
11 

25 

'9 
20 
17 
32 
19 
36 

11 
21 
13 
29 
22 
41 
24 
46 

19 
37 
22 
41 

TABLE    V. 

Total  Loads  in  Thousands  of  Pounds, 
Allowed  on  Single  Angles  as  Com- 
pression Members* 

Size  of 
Angle. 

Unsupported    Length    of    Member. 

4  ft.        5  ft.    |    6  ft. 

7  ft.        8  ft. 

9ft.    | 

10  ft. 

4     x4     x3/& 
4     x4     x^ 
6     x6     xys 
b     x6     x$4 
8     x8     xl/2 
8     x8     x£4 
5     x3     xH 
5     x3     x^ 
5     x3y3xH 
5     x3y2xM 
6     x3^x^ 
6     x3y2x& 
6     x4     x^ 
6     x4     x£$ 
8     x6     xy2 
8     x6     x^ 

33 
63 
56 
108 
104 
154 
31 
59 
35 
67 
40 
75 
43 
83 
88 
129 

31 
58 
54 
103 
101 
149 
28 
53 
32 
61 
37 
69 
41 
77 
85 
124 

28 
53 
51 
98 
97 
143 
25 
47 
30 
56 
33 
63 
38 
72 
81 
119 

26 
48 
48 
93 
94 
138 

23 
43 
46 
88 
90 
133 

21 

38 

IS 
34 

43 
83 

87 
128 

41 
78 
84 
123 

22 
41 

19 

35 
24 
45 
27 
51 

21 
40 
24 
45 

26 
49 
66 
97 

27 
51 
30 
57 

35    "1      32           29 
66           61            55 
77           74           70 
113          108          102 

34 


TABLE    VI. 

Total  Load  in  Thousands  of  Pounds, 
Allowed   on   Two  Angles  Placed 
Thus     ip    Seperated  i  in,,  as 
Com           pression  Members, 

Size  of 
Angles.       j 

Unsupported    Length    of    Member. 

4  ft.        5  ft.        6  ft.        7  ft        8  ft. 

9  ft   |  10  ft. 

2^x2     xy4\ 

2y2x2   xy2\ 
3   x2y2Xy4\ 
3    x2y2xy2< 
3y2x2y2xy4 
3y2x2y2xy2 

3y2x3     x3/8 
3l/2x3     x3/4 
4     x3     x3/8 
4     x3     x3/4 
5     x3     x3/8 
5     x3     x3/4 
5     x3y2x3/s 
5     x3y2x3/4 
6     x3y2x3/8 
6     x3l/2xy4 
6     x4     x3/8 
6     x4     x3/4 

25 
46 
32 
61 
37 
70 
58 
108 
64 
121 
74 
143 
81 
156 
91 
175 
98 
189 

23 
42 
30 
57 
35 
66 
55 
102 
62 
116 
71 
138 
79 
151 
87 
169 
95 
183 

21 
39 
28 
53 
33 
63 
52 
97 
59 
111 
68 
132 
76 
145 
84 
163 
92 
178 

19 

35 
26 
50 
31 
59 
49 
91 
56 
105 
65 
126 
73 
140 
81 
157 
89 
172 

17 
31 
24 
46 
29 
56 
46 
85     • 
53 
100 
62 
121 
70 
135 

151 
86 
167 

15     1 

44 

s1 

52 
43 
80 
51 
94 
59 
115 
67 
130 
74 
145 
83 
161 

21 
38 
"16  
49 
41 
74 
48 
89 
56 
110 
65 
124 
71 
139 
80 
156 

TABLE   VII. 

Total  Load  in  Thousands  of  Pounds, 
Allowed    on   Two   Angles   Placed 
Thus  .^  ——  ^  .  as  Compression 
••        Members, 

•Size  of 
Angles. 

Unsup 

ported    Length    of    Member. 

4  ft.        5  ft. 

6  ft.    |    7  ft        8  ft. 

9  ft    |  10  ft. 

2^x2     xJ4 

2y2x2    xy2 

3   x2y2xy4 
3    x2y2xy, 
3y2x2y2xy4 
3y2x2y2xy2 

22 
1      41 
|      30 
57 
33 
62 
i      56 
103 
60 
112 
68 
128 
I      76 
|    144 
|      85 
|    161 
I      93 
|    176 

20 
36 
28 
52 
30 
56 
52 
96 
56 
104 
63 
118 
72 
135 
80 
151 
88 
168 

17 
31 

15 

26 

20 
37 

22 
40 

18 
33 
19 

34 

25 
47 
27 
51 
49 
89 
52 
96 
59 
109 
68 
127 
75 
141 
84 
159 

23 
42 
24 
45 
45 
82 
48 
88 
54 
99 
64 
119 
70 
131 
|      80 
151 

3y2x3     xY» 
3l/2x3     x3/4 
4     x3     x3/s 
4     x3     xy4 
5     x3     x3/8 
5     x3     x3/4 
5     x3y2x3/s 
5     x3y2x3/4 
6     x3y2x3/8 
6     x3y2x3/4 
6     x4     xH 
6     x4     x% 

41 
75 
44 
80 
49 
90 
59 
111 
65 
122 
75 
142 

38 
67 
40 
73 

3* 
60 
36 
65 
40 
71 

44 
80 

55 
102 
61 
112 
71 
133 

51 
94 
56 
102 
67 
125 

TABLE  VIII. 

Total  Load  in  Thousands  of  Pounds, 

Allowed  on  Two  Angles 

Placed  Thus 

•"ip"  as  Compression  Members. 

Size  of 
Angles. 

Unsup 

ported    Length 

of    Member. 

4  ft.    |    5  ft. 

6  ft.        7  ft. 

8  ft. 

9  ft      10  ft. 

2     x2     xJ4|     20 

18 

16 

14 

2     x2     xHJ     29 

25 

22 

19 

2l/2x2y2xIA\     28 

25 

23    " 

21 

]     19 

.  . 

.  . 

2l/2x2l/2Xl/2\     51 

47 

43 

39 

1     35 

3     x3     xJ4|     35 

33 

31 

29 

27 

24 

22 

3     x3     x^|     81 

76 

|     70 

65 

60 

54 

49 

3y2xZi/2x^\    62 

59 

56 

53 

50 

46 

43 

3^x3^x341    117 

111 

105 

98 

92 

86 

79 

4     x4     x3/£ 

74 

71 

68 

64 

61 

58 

55 

4     x4     xfa 

140 

134 

127 

121 

114 

108 

102 

6     x6     x3/& 

120 

116 

113 

110 

107 

104 

100 

6     x6     xY* 

231 

224 

218 

212 

205 

199 

192 

8     x8     x*/2 

218 

214 

210 

205 

201 

197 

192 

8     x8     x34 

322 

316 

309 

303 

296 

290      I    283 

TABLE  IX. 

Total  Load  in  Thousands  of  Pounds, 

on   Four   Angles  Placed 

Thus 

JL  as  Compression  Members, 

Size  of 
Angles. 

Unsupported    Length 

of    Member. 

4  ft.        5  ft.    | 

6  ft.        7  ft. 

8  ft. 

9  ft   |  10  ft. 

2     x2     xl/4 

45 

42 

39 

36 

33 

29 

26 

2     x2     xys 

65 

61 

57 

52 

48 

44 

39 

2y2x2l/2x% 

60 

57 

53 

50 

47 

44 

~Ti  

2y2x2l/2xl/2 

114 

108 

103 

97 

91 

86 

80 

3     x3     xy4 

75 

72 

68 

65 

62 

59 

56 

3     x3     x54 

176 

169 

162 

155 

148 

141 

133 

3l/2x3I/2x3/& 

132 

127 

123 

118 

113 

109 

104 

3I/2x3l/2x3/4 

251 

243 

234 

226 

217 

209 

200 

4     x4     x3/s\    155 

150 

145 

141 

136 

131 

126 

4     x4     xY*\   296 

287 

279 

270 

261 

252 

244 

6     x6     xYz     246 

241 

236 

231 

226 

221 

216 

6     x6     -X.YA.     476 

467     1 

458 

449 

439 

430 

421 

•8     x8     xy2\   445         439      j 

432 

426 

419 

413 

406 

8     x8     xY4\   658         648     | 

639      I   629      j 

620 

610      !    601            ' 

36 


TABLE    X. 


Total  Load  in  Thousands  of  Pounds, 

Allowed  on  Standard  Gas  Pipe  as 

Compression  Members, 


Nominal       External  I  Internal 

Size  of        Diam.  in  f   Diam.  in 

Pipe.  In.        |         In. 


Unsup.     Lgth.     of     Member. 


|  5  ft.  |  6  ft.  |  7  ft.  |  8  ft.  |  9  ft.  1 10     ft. 


2.375 
2.875 
3.500 
4.000 
4.500 
5.000 
5.563 
6.625 
7.625 
8.625 
9.625 
10.750 


t"W 


TABLE    XI. 

r-T.  Total  Load  in  Thousands 

of  Pounds  Allowed  on 

Bethlehem  H-Sections 

as  Compression 

Members* 


I  mn.  in  In.  and  Weight  of  Sec. 


D 

B 

T 

w 

Weight 
in   L,bs.  ! 
per  Ft. 

Unsupported   L,gth. 

of    Member. 

10ft|12ft|14ft|16ft|18ft 

20ft. 

8 

8.00|    ya\    .31|      34.5 

119 

1  12 

105 

98 

91 

84 

8l/2 

8.16|    34 

.47 

53.0 

184 

173J    163 

152 

142 

132 

854 

8.24 

H 

.55 

62.0 

217 

205 

192 

180 

168 

156 

9 

8.32 

i 

.63 

71.5 

251 

237  j    223 

209|    196 

182 

9l/2 

8.47 

1  14 

.78 

90.5 

320 

302 

285 

268 

251 

234 

10 

10.00 

>M$ 

.39 

54.0 

198     189 

180 

171 

162|    153 

10J4|10.08 

M 

.47 

65.5 

240|    229|    219|    208|    197|    187 

\Ql/2 

10.16 

% 

.55 

77.0 

282 

270 

258 

246 

234 

221 

11 

10.31 

1  1A 

.70 

99.5 

368 

352 

3371    321 

306!    290 

11J4I10.47 

\y^ 

.86 

123.5 

457 

4381    4201    401 

3811    363 

1  1  54  1  1  1  .  92 

$i 

.39 

64  .  5 

244J    235|    227|    2181   209|    200 

12      |12.00 

y* 

.47|      78.0 

296|    285|   274|    264|   253|    243 

\2l/2 

12.16|1 

.63|    105.0 

400|    386|    372 

358 

344|    330 

13 

12.31|1J4 

.78|    132.5 

506|   4881    471 

453 

4361   418 

143/6114 
153/6114 


14 


.47 
.96 
.1211 


.94| 
.471 
.63! 
.94! 
.74|2  |1.25| 
.90 1 2 '/ill.  41 1 


161.0 
91.0 
122.5 
186.5 
253.0 
287.5 


|  6151  5951  574|  5531  533  512 

|  353|  343|  332|  321|  311|  300 

I  477|  463|  449|  435]  421 |  407 

730|  710|  6891  668J  647|  626 

994|  966|  9391  911!  884|  856 

1130!1099|1069|1038!1007!  976 


TABLE    XIII. 

H    Total  Load  in  Thousands  of 
Pounds     Allowed     on    I- 
Shaped  Sections  as  Com- 
pression Members. 

Web.                Angles. 

Unsupported    l^ength    of    iVieiiiu>  .. 

10ft.    12ft.    14ft.|16ft.    18ft.|20it. 

12xA 

12xA 
12x^ 

12xA 
12xA 

12x^ 

12xA 
12xT85 
12x^ 
12x3/6 
12x3/S 
12x34 

I4x  A 

14xT5s 
14xJ* 
14xA 
14xA 

14xj4 
14Xl5g 
14xA 
14x^ 
14x3/g 
14x3/6 
14x34 
14x3^ 
14x3^ 
14x34 
16X1S5 
16xA 
16x^ 
16X15S 
16xA 
16x^ 
16x3/6 
16x3/6 
16x34 
16x3^ 
16x44 
16x34 

3^x3     xA 
3^x3     x^ 
3^x3     xya 
4     x3     xA 
4     x3     xj^ 
4     x3     xj4   . 
5     x3     xA 
5     x3     xj^ 
5     x3     xl/2 
6     x3l/2x3/s 
6     x3#x# 
6     x3>ax34 

3^x3     xA 
3^x3     x^ 
3^x3     x>S 
4     x3     x*s 
4     x3     xj^ 
4     x3     x^a 
5     x3    xA 
5     x3     x^ 
5     x3     xl/2 
6     x3j4x5^ 
6     x3^xM 
6     x3j4x^ 
6     x4     x?/6 
6     x4     x34 
6     x4     x?4 
4     x3     x,5c 
4     x3     x^ 
4     x3     x# 
5     x3     xA 
5     x3     xj^ 
5     x3     x>i 
6    x3!4x3^ 
6     x3^x34 
6    x3j4x# 
6     x4     xJ'g 
6     x4     x-)4 
6     x4     x^ 

115 
164 
186 
131 
186 
210 
158 
226 
252 
227 
391 
446 
120 
169 
194 
136 
192 
219 

165 
233 
262 
235 
399 
463 
244 
417 
481 
142 
198 
228 
171 
239 
272 
244 
408 
480 
252 
425 
498 

103 
149 
168 
120 
173 
194 
149 
214 
238 
217 
375 
428 
107 
153 
176 
125 
178 
202 

155 
220 
248 
225 
383 
444 
232 
400 
460 

129 
182 
210 
160 
226. 
257 
232 
391 
460 
240 
408 
477 

91 
134 

151 
109 
159 
178 

140 
203 
225 
207 
360 
410 

79 
119 
133 

99 
146 
162 
131 
191 
211 
197 
345 
392 

104 
116 
88 
132 
146 

122 
179 
198 

187 
329 

375 

77 
118 

130 

113~ 
167 
184 

177 
314 
357 

94 
137 
157 
113 
163 
184 

145 
208 
233 
214 
368 
425 
221 
383 
440 

117 
167 
191 
150 
213 
241 
221 
375 
440 
228 
390 
455 

81 
121 
138 

105 
119 
90 
135 
150 

120 

133 

102 
149 
167 

136 
196 
219 
204 
352 
406 
210 
365 
420 

126 
183 
204 
193 
336 
387 
199 
348 
400 

117 
171 
190 
183 
320 
368 
188 
331 
3PO 

105   1 
152 
173  | 
140 
200 
226 
210 
358 
420 
217 
372 
434 

92 
137 
155 

l22 

137 

130 
187 
210   j 
199 
342 
400 
205 
355 
413 

119 
175 
195 
188 
326 
380 
193 
337 
392 

38 


TABLE    XII. 

H     Total    Load   in   Thousands 
of  Pounds  Allowed  on  I- 
Shaped  Sections  as  Com- 
pression Members. 

Web. 

Angles. 

Unsupported    Length    of    Member. 

8  ft.    10  ft.    12  ft.    14  ft.    16  ft.    18  ft. 

6xI/4 

2l/2x2     xJ4 

56 

48 

41 

6xy4 

2^x2     xj4 

98 

87 

75 

64 

6xy2 

2l/2x2     xJ/2 

114 

101 

87 

74 

7xy4 

2y2x2     x  T4 

58 

50   ,      42 

7xI/4 

2  Kx2     xJ/2 

100 

88 

76 

64 

7xl/2 

2J/ax2     x}4 

118 

104 

90 

76 

8xy4 

2y2x2     xVi 

60 

51 

42 

8xT/4 

2^x2     xj4 

102 

90 

77 

*65 

8xy2 

2j^x2     x^ 

122 

107 

92 

77 

8xy4 

3   x2y2xy4 

76 

68         59 

51 

8x*4 

3     x2j^x^ 

132 

119       106 

94 

81 

8xy2 

153 

138 

124 

109 

94 

9x  B 

3     x2l/x  B- 

98 

87 

77 

66 

.  .  . 

9XJ? 

3     x2pxj/ 

140 

126 

112 

99 

85 

9xi| 

3     x2>|x^| 

158 

142 

126 

111 

95 

9x  5 

3*/x2y2x  5 

113 

103 

93^ 

84 

74 

65 

9xi5ff 

3y2yt2y2xy2 

160 

148 

136 

123 

111         98 

9xJ^ 

3y2x2y2x.y2 

179 

165 

151 

137 

123       109 

9x  5 

3y2x3     xA 

118 

108 

97 

87 

76       ... 

9x  5 

170 

156 

143 

129 

115       101 

9xV£ 

3y2x3    x^z 

189 

174 

158       143 

127       112 

9xT5s 

4     x3     XTBS 

132 

123       113       104         94  \     85 

9xJL 

4     x3     x}4 

190 

178 

165 

153 

140    \    128 

f)xy2 

4     x3     x^ 

210 

196 

182 

168 

154       140 

9x  B 

5     x3     x-fg 

156 

148 

140 

132 

124 

116 

9XT5ff 

5     x3     xj4 

227 

216 

205 

195 

184 

173 

5     x3    x^ 

248 

236 

224 

212 

199 

187 

10xW 

3^x3     XTBS 

121 

110 

99 

88 

77 

10xW 

3^x3     xy2 

173 

159 

145 

131 

117 

103 

10x^4 

3y2x3     x/2 

194 

178 

162 

146 

130 

114 

lOx  B 

4     x3     xA 

135 

125 

115 

105 

96 

86 

JQX\ 

4     x3     x^ 

194 

181 

168 

155 

142 

129 

10xJ^ 

4     x3     xj^ 

215 

200 

186 

171 

156 

142 

lOx  B 

5     x  3     x  i  % 

160 

152       143       135 

127  ' 

118 

1  0x  5 

5     x3    xy2 

231 

220       209       197 

186 

175 

10xl| 

5     x3     xj^ 

254 

241       228 

216 

203 

191 

10x3/1 

6     x3^x-K 

228      219 

209 

200 

191 

182 

10x3^ 

397       382 

367 

352 

338 

323 

6     X3K.X54 

446       429 

412 

395 

379 

362 

39 


H 


TABLE    XIV. 


Total  Load  in  Thousands 

of  Pounds   Allowed   on 

I-Shaped  Sections  as 

Compression  Members. 


|    Cover 
Web.     Aneles.  |  Plates. 


Area  |l,.R's|  Unsup.  Lgth.  of  M'b'r. 
in      |    of      |    10|    12]    14|    16     18]    20 
sq.in.]  Gyr.  |  ft.  |  ft.  |  ft.  |  ft. 


8x 


11.24|  1.68|124|115|106|   96|   87|    78 

15.24  1.86|175J163il52|140|129|118 

20.00J  1.78  226J210  195  179  163|  148 

22.00|  1.74|246|229|211|194|176il58 


9x4 


11.74] 
16.24] 
21.00] 
23.00] 

14.92)" 
18.29] 
21.81] 
23.50] 


1.86|135 
2.09|193 
1.97|245 


126|117|108|  99  |  91 
182|  171  |  160|  150|  139 
230|215|201  |  186|  171 


1.92|266|250|233 1 2J  6j  20  0 1 1 8  3 
1.86|l71|160|149|i37|T2fa|il5 
2.01|215]202|189|177|164|151 
1.94)253 |238|222| 206] 191 j 175 
1.90)271 1 254 1 237 1 219] 202) 185 


2.05|183|173|162|152|141|131 
2.24|233|221|209|197|185|173 
2.15|273|258|243|229|214|199 
2. 09)291 | 274 | 258)242] 226|20 9 
1.91|187|175|163|151|140|128 
2.04|230j217j204|190|177(16-4 
1.99|279|262|245|229|212|195 
1.95  297  278 | 260 | 242 j 224 | 206 


16.78]  2.08|199|188|176J165|154|143 

20.53J  2.25  249]  236]  223  1210|  198]  185 

24.81|  2.17|298|282|266|250|234|218 

26.50]  2.13]316|299|282|264|247|230 


9xA|4x3 
9x^14x3 


16.80]  2.  02]  198]  186]  174]  163]  15  1|14U 

20.17]  2.  11|240|227|213|200|187|174 

24.81|  2.10|295]279|262|246|229|213 

26.50]  2.07)314)296  278)  260  |242|  225 


9xT58|4x3     xftUOxft 
9xA|4x3 
9xA  4x3 
9x^  4x3     x 


17.42|  2.17|209|198]187|175]164|153 

21.17]  2.32|258|246|233|220!208|195 

25.81]  2.  26]  313]  297  |281|265|249|  233 

27.50]  2.22  332)  315)  297  |  280]  263]  246 


10xA|4x3 
10xft|4x3 
10xA|4x3 


17.74]  2.15)212  201  |  189)  178]  166]  155 

21.49]  2.30|262|249|236|223|210|197 

26.13]  2.  25  |316|300|  284  J268|252|236 

28.00]  2.20I337|319|302|284|266|248 


10xA|4x3 


18.36]  2.33|224|213|202|191|1.80|169 

22.49|  2.50|279|267|254|242|229|217 

27.13]  2.  43  |  335  |  31  9)304]  288]  273)  257 

29  .  00  |  2  .  37  |  356  |  339  |  322  |  305  |  287  |  270 


40 


TABLE    XV. 

H   Total    Load   in   Thousands 
of  Pounds  Allowed  on  I- 
Shaped  Sections  as  Com- 
pression Members. 

I           I 

Cover 
Web.    Angles.  |  Plates. 

Area  |L.R's|  Unsup.  L,gth.  of  M'b'r. 

in         of     |    10|    12)    14|    16     18 
sq.  in.  |  Gyr.  |  ft.  |  ft.  |  ft.  |  ft.     ft. 

20 
ft. 

10x3^  |6x3Hx3/6  |13x3/g 
10x3x3  1  6x3^x3/3-1  13x34 
1  Ox  ^  16x3x^x34)  13x34 
10x^|6x3Hx34|13x34 

27.18     3.07|351|339|327|315|302|290 
36.93     3.27|483|467|451|436|420|404 
49  .  49     3  .  22  j  645  1  624  1  603  581  j  560  1  538 
50.74     3.  21  |661  |  639  \617\  595  |  573)  551 

10x3/^|  6x3^x3/8  j  14x3^ 
10x3/6  \6x3y2xys\  14x34 
10x3,8  |6x3/^x34|  14x34 
10x^)6x3x^x34)14x34 

27.93     3.23|364|352|340|328|316|304 
38.43]    3.47J507  492)476  461  J445J430 
50.99J    3.38|670  649)628  |607|S86|56S 
52.24J    3.  36  |686|664  |643  |621  |599  |578 

12x^1  4x3     xT5s   12xf6 
12xTB6(4x3     xft|12x# 
12xTss|4x3     xy2\12xy2 
12x^14x3     xy2\l2xy2 

19.61|    2.  48)  243)  232)  221)210]  199)  188 
24.11  |   2.69|304|292|279|267|254|242 
28.75|   2.59|360|344|329]314  298)283 
31.001    2.52  386)368  351  334  317|300 

12xft|4x3     xT5s|13xT5s 
12x^(4x3     xT58|13xK 
12x&|4x3     xK(13xH 
12xH|4x3     x^|13xH 

20.24]    2.  67  |  255  |244|  234  |223I213|  202 
25.11|   2.91|322|310|298|286|274|262 
29.75]   2.  79  J378J363  (348)333  |319|  304 
32.00]   2.  71  |404|388|371  |  355)  338)  322' 

l2x3/8\bx3l/2x3/8\13x3/8 
12x3^16x3^x3^113x34 
12x3^  |6x3^x34|  13x34 
12x^16x3x^x34)13x34 

27.93     3.03)360)3481330,32213091296 
37.68     3.23  492(475  459  4431427  410 

50.24J    3.20  655|633|611|589  567)545 
51.74)    3.18|673|651|628|605  583)560 

12x3^16x3^x3^114x3^ 
12xM|6x3^x^|14x34 
12x3^|6x3^x34|14x34 
12x^16x3^x34  |14x34 

28.68)    3.  18)  373)361  |348)336|  323]  310 
39.18]    3.43i516|500j484|468|453|437 
51.74]    3.  36)  679]  658]  636]  615]  594]  572 
53.24]    3.  33  |698|676|653  |631|609|  587 

14x^(4x3     xT55|14xT5ff 
14x^4x3     x/g|14xH 
14x?6|4x3     xy2\l4xy2 
14x^14x3     xy2   Hx'X 

21.49]    2.  84  |  274  |  263  |  253)  242]  232]  221 
26.74]    3.11|347|335|323|311|299|287 
31.38]   2.  97)404]  389)  374)  359]  345(330 
34.00]   2.  88  (435  |  418(402(385]  369]  352 

14Xlss!4x3     xi'5   ISxfu 
14x^5  1  4x3     xjis  jlSx^ 
14xTS6  4x3     x^|15x>i 
14xK  4x3     xy2\l5xy2 

^2.11     3.  05  (286  (276(265  |  255)  245)235 
27.74     3.  35  |  364(353)  341  )  329(31  8)  306 
32.38     3.  19  |422)407  |393|379|  365)  351 
35.00     3.  09  |453|437|422  (406  (390(374 

14xl/8  |6x3^x3,^j  14x^8 
14x  ys  \6x3y2xi/s  |14x34 
14x3^16x3^x3x4)14x34 
Hx^  16x3^x34  |14xM 

^9.43|    3.14|382|369J356|343  330 
39.931    3.40|525|509|493|476  460 
52.49|    3.33|688|666|644|622|600 
54.24)    3.30|710|687|664|641|618 

317 
444 
578 
596 

14x3^16x3^x^)15x3^ 
14x3^|6x3Hx3^!l5x34 
14x3^|6x3Hx34|15x34 
14x^1  6x3  '4x34  |15x34 

30.18|   3.  31  (395  (383  (370  j  357)  345  (332 
41.43     3.  61  (550  |534|  5181  502(486(470 
53.99     3.  50(71  3  |692|670  |649|  627  1606 
55.74!    3.  47  |735|713  1691  1668  |646|  624 

41 


TABLE   XVI. 

Total   Load   in   Thousands 

•9 

Cof  Pounds   Allowed   in 
Latticed  Channel  Sec- 
tions as  Compression 

Members. 

D 

not  less  than  .65  of  the  depth  of  channel. 

Sizeof  Channels. 

Unsupported  Length  of  Member. 

Depth 

Weight  in  Ubs. 

in 

In. 

per  Foot. 

10ft.    12ft.    14ft.    16ft.    18  ft.)  20  ft. 

s 

6.5 

45         43         40         37         34         31 

5 

9.0 

60 

56 

52 

48 

44          40 

5 

11.5 

76 

70 

65 

60 

54   |      49 

6 

8. 

58 

55 

53 

50 

47    |      44 

6 

10.5 

74 

71 

67 

63 

59         55 

6 

13.0 

91 

86 

81 

76 

71 

66 

6 

15.5 

108 

102 

96 

90 

83 

77 

7 

9.75 

72 

69 

66 

63 

60 

57 

7 

12.25 

90 

86 

82 

78 

75 

71 

7 

14.75 

108 

103 

98 

93 

88 

84 

7 

17.25 

125 

119 

114 

108 

102 

96 

7 

19.75 

143 

136 

129 

122 

116 

109 

5 

? 

11.25 

87 

84 

81 

78 

75 

72 

3 

13.75 

104 

100 

96 

93 

89 

85 

16.25 

122 

118 

113 

108 

104 

99 

8 

18.75 

140 

135 

129 

124 

119 

113 

1 

3 

21.25 

159 

152 

146 

140 

133 

127 

9 

13.25 

103 

100 

97 

93 

,90         87 

9 

15.00 

116 

112 

109 

105 

102 

98 

9 

20.00 

153 

148 

143 

138 

133 

128 

9 

25.00 

190 

184 

177 

171 

164 

157 

10 

15.00 

120 

116 

113 

110 

107       103 

1( 

) 

20.00 

156 

152 

147 

143 

138       134 

10 

25.00 

194 

189 

183 

177 

171       165 

10 

30.00 

232 

225 

218 

211 

204 

196 

10 

35.00 

270 

261 

253 

244 

236 

227 

12                 20.50 

165 

161 

158 

154       151 

147 

12                 25.00 

200 

196 

191 

186 

182 

177 

12                 30.00 

239 

234 

228 

222 

216 

211 

12 

35.00 

278 

272 

265 

258 

251 

244 

12 

40.00 

317 

309 

301 

293 

285 

277 

15 

33.00 

277 

272       267 

262 

257 

252 

15 

35.00 

287 

282       277 

272 

267 

261 

15 

40.00 

327 

321 

315 

309 

303 

297 

15 

45.00 

368 

361 

354 

347 

340 

333 

15 

50.00 

408 

400 

392 

384 

377 

369 

15 

55.00 

448 

439       431 

422 

413 

405 

42 


TABLE   XVII. 

n     Total  Load  in  Thousands  of 
Pounds  Allowed  on  Channel 
and    Plate    Sections    as 
Compression  Members. 

Size  of  Channels 

Size 
of 

Unsupported  Length  of  Member. 

Depth 
in 

Weight 
in  Lbs. 

In. 

per  Ft. 

Plates. 

10  ft.    12  ft.    14  ft.    16  ft. 

18  ft.   20  ft. 

7 

9.75 

9x^4 

128 

123 

118       112 

107       102 

7 

9.75 

9xl/2 

185 

177 

169       161 

154       146 

7 

12.25 

9xj55 

161 

154 

147       140 

133       126 

7 

12.25 

9xT95 

217       208 

198       189 

180       170 

7 

14.75 

9x3/6 

192 

184 

175       167 

158       150 

7 

14.75 

9xys 

248 

238 

227 

216 

205       194 

7 

17.25 

9xT7ff 

224 

213 

203 

193 

183       173 

7 

17.25 

9xfi 

280 

267 

255 

242 

230       217 

7 

9.75 

11x54 

146 

141 

136 

131 

126       122 

7 

9.75 

Hx}/2 

219 

212 

205 

198 

192 

185 

7 

12.25 

llxT5s 

183 

177 

171 

164 

158 

152 

7 

12.25 

llxft 

257 

249 

240 

232 

224 

216 

7 

14.75 

llx^ 

220 

212 

205 

197 

190 

182 

7 

14.75 

llx^g" 

294 

284 

275 

265 

256 

246 

7 

17.25 

llx/ff 

257 

248 

239 

230 

221 

213 

7 

17.25 

Hx}£ 

330 

319 

309 

298 

287 

276 

8 

11.25 

10x^4 

151 

146 

140 

135 

129 

124 

8 

11.25 

215 

207 

199 

192 

184 

176 

8 

13.75 

10x^5 

184 

177 

171 

164 

157 

151 

8 

13.75 

10xT9ff 

248 

239 

230 

221 

212 

203 

8 

16.25 

10x3^ 

219 

211 

202 

194 

186 

178 

8 

16.25 

283 

272 

261 

251 

240 

230 

8 

18.75 

lOx-fe 

253 

243 

233 

224 

214 

205 

8 

18.75 

lOxji 

317 

305 

293 

281 

269 

257 

8 

11.25 

12x^4 

169 

164 

159 

154 

149 

144 

8 

11.25 

l2xl/2 

249 

242 

235 

228 

221 

214 

8 

13.75 

12xT5ff 

207 

201 

195 

189 

183 

177 

8 

13.75 

12x& 

287 

279 

271 

263 

255 

246 

8 

16.25 

12x3/3 

246 

239 

232 

224 

217 

210 

8 

16.25 

327 

317 

308       298 

289 

280 

8 

18.75 

12xT75 

285 

277 

268 

260 

252 

243 

8 

18.75 

366 

355 

344 

334 

323 

313 

43 


TABLE  XVIII. 

n  Total    Load    in    Thousands    of 
Pounds  Allowed  on  Channel 
and  Plate  Sections  as  Com- 
pression  Members. 

Size  of  Channels) 

Unsupported    Length    of    Member. 

Depth 

Weight 

Size 

£ 

in 
In. 

in  Lbs. 
per  Ft. 

OI 

Plates. 

10ft.    12ft.    14ft.|16ft.    18ft.|20ft. 

9         13.25 

llxJ4 

175 

169       164 

158 

153 

147 

9         13.25 

llxtf 

246 

238 

231 

223 

215 

207 

9         15.00 

llxT5ff 

206 

199 

193 

186 

180 

173 

9 

15.00 

llxA 

278 

269 

260 

251 

242 

233 

9 

20.00 

1  1*8 

261 

253 

244 

235 

227 

218 

9 

20.00 

llxfc 

333 

322 

311 

300 

289 

278 

9 

25.00 

Hxft 

316 

306 

295 

284 

274 

263 

9 

25.00 

Hxli 

388 

375 

362 

349 

336 

322 

9 

13.25 

13xK 

192 

188 

183 

178 

173 

168 

9 

13.25 

13xH 

280 

273 

266 

259 

252 

245 

9         15.00 

13xft 

229 

223 

217 

211 

205 

199 

9         15.00 

13xA 

316 

308 

300 

292 

284 

275 

9 

20.00 

13x^ 

289 

281 

274 

266 

259 

251 

9 

20.00 

13x§^ 

377 

367 

357 

347 

338 

328 

9 

25.00 

13x* 

350 

340 

331 

322 

312 

303 

9 

25.00 

Uxg 

438 

426 

414 

403 

391 

380 

10 

15 

12xA 

219 

213 

207 

201 

195 

189 

10 

15 

12xA 

298 

290 

281 

273 

264 

256 

10 

20 

I2x« 

276 

268 

260 

252 

244 

236 

10 

20 

12x^ 

355 

345 

335 

324 

314 

304 

10 

25 

12x^r 

334 

324 

314 

305 

295 

285 

10 

25               12xH 

413 

401 

389 

377 

364 

352 

10 

30 

12x^ 

392 

380 

368 

356 

345 

333 

10 

30 

12x^4 

471 

457 

443 

428 

414 

400 

10         15               14x^ 

241 

236 

230 

225 

220 

214 

10         15               14xT9ff 

336 

328 

320 

312 

305 

297 

10         20               14xM 

304 

297 

290 

283 

276 

269 

10         20               14x^ 

398 

389 

379 

370  " 

360 

351 

10         25 

14xft 

367 

358 

350 

341 

333 

324 

10 

25 

14xjJ 

461 

450 

439 

428 

417 

406 

10 

30 

14x^ 

430 

420 

410 

399 

389 

379 

10         30 

14x& 

524 

512 

499 

487 

474 

461 

44 


TABLE  XIX. 

..    Total    Load    in    Thousands    of 
Pounds  Allowed  on  Channel 
and  Plate  Sections  as  Com- 
JL—  |  JHB              pression  Members. 

Size  of  Channels 

Size 
of 

Unsupported   Length   of   Member. 

Depth 
in 

Weight 
in  L,bs. 

In. 

per  Ft. 

Plates. 

10  ft. 

12ft.    14  ft.  |  16ft.  |  18ft.  |  20  ft. 

12 

20.5          14x3/3 

307 

300 

293 

286 

278 

271 

12 

20.5 

14x^ 

401 

392 

382 

373 

363 

354 

12 

25 

!4xA 

366 

357 

349 

340 

331 

323 

12 

25          |    14xH 

460 

449 

438 

427 

416 

405 

12 

30          |    14x}4 

429 

419 

408 

398 

387 

377 

12 

30 

14x3/4 

523 

510 

498 

485- 

472 

459 

12 

35 

14xA 

492 

480 

468 

456 

443 

431 

-8- 

35 

Hx}2- 

586 
333- 

572 

"127" 

557 

543 

528 

514 

20.5 

16x3/8 

320 

314 

307 

301 

12 

20.5 

I6x^ 

443 

434 

425 

416 

407 

399 

12 

25 

16xTV 

397 

389 

381 

373 

366 

358 

12 

25 

16xH 

507 

496 

486 

476 

466 

456 

12 

30 

16x# 

465 

456 

446 

437 

428 

418 

12 

30 

16x?4 

574 

563 

551 

539 

528 

516 

12 

35 

16x& 

533 

522 

511 

500 

489 

479 

12 

35 

16xif 

642 

629 

616 

602 

589 

576 

15 

33 

17xTV 

483 

475 

466 

457 

448 

439 

15 

33 

17xft 

601 

589 

578 

567 

556 

545 

15 

40 

17x^ 

564 

553 

543 

533 

522 

512 

15 

40 

17x34 

681 

668 

656 

643 

630 

617 

15 

45 

17xrk 

634 

622 

610 

599 

587 

575 

15 

45 

17xl| 

751 

737 

723 

709 

695 

680 

15 

50 

17x54 

704 

690 

677 

664 

651       637 

15 

50 

I7x7/s 

821 

805 

790 

774 

758       743 

15 
15 

33 

33 

19x& 
19x» 

513 
646 

505 
636 

497 
625 

489 
615 

481    |  473 
604    |   594 

15 

40 

19x^ 

599 

589 

580 

570 

561       551 

15 

40 

19x54 

731 

719 

708 

696 

684       672 

15 

45 

19xft 

674 

663       652 

641 

630       619 

15 

45 

19x|| 

806 

793    |   780 

767 

753       740 

IS 

50 

19x5% 

748 

736       724 

711 

699       687 

15           50             19x7/& 

880 

866       851 

837 

822       808 

45 


TABLE  XX. 

H  Total  Load  in  Thousands  of 
Pounds  Allowed  on  Zee- 
Bar  Columns* 

Width  of 
Web  Plate 

Webof|Thick- 
Z-Bar   |   ness 

Unsupported  Length  of  Column. 

in   In. 

in  In. 

of 

Metal 

10ft.    12  ft.  |14  ft.    16ft.    18  ft.  |  20  ft. 

6 

3 

54 

107 

100   |     93 

86 

79 

72 

6 

3 

I5e 

136 

128   |    119 

110 

102 

9.-: 

6 

3 

In 

157 

147 

137 

127 

116 

106 

6 

3 

& 

186 

174 

163 

151 

139 

128 

6 

3 

H 

205 

192 

178 

165 

152 

139 

6 

3 

S 

234 

219 

205 

191 

176 

162 

7 

4 

ft 

141 

134   |    128 

122 

115 

109 

7 

4 

v\ 

178 

170 

162 

154 

146 

138 

7 

4 

y» 

215 

206 

196 

187 

178 

168 

7 

4 

2 

239 

228 

217 

206 

195 

185 

7 

4 

S 

276 

263 

251 

239 

227 

215 

7 

4 

ft 

313 

299 

286 

272 

259 

245 

7 

4 

8 

330 

316 

301 

286 

271 

257 

7 

4 

H 

367 

351 

335 

319 

303 

287 

7 

4 

M 

404  1   387 

370 

353 

336 

319 

7 

5 

A 

204   |    197   |    190 

183 

176 

169 

7 

5 

H 

247       238   |    230 

222 

213 

205 

7 

5 

<& 

290 

280 

271 

261 

251 

241 

7 

5 

Vz 

317 

306 

295 

284 

273 

262 

7 

s 

& 

360 

348 

335 

323 

311 

299 

7 

s 

ii 

403       390 

376 

363 

350 

336 

7 

5 

u 

424 

409 

395 

380 

366 

351 

7 

5 

M 

466 

450 

435 

419 

403 

388 

7 

5 

ft 

509   j   492 

476 

459 

442 

425 

8 

6 

Hi 

284 

276 

268 

260 

252 

244 

8 

6 

S 

334 

325 

315 

306 

297 

287 

8 

6 

s 

384 

373 

363 

352 

342 

331 

8 

6 

& 

416 

404 

392 

381 

369 

357 

8 

6 

465 

452 

439 

426 

413 

401 

8 

6 

Jl 

515 

501 

486 

473 

458 

444 

8 

6 

^ 

540 

525 

510 

495 

479 

464 

8 

6 

11 

589 

572 

556 

540 

523 

507 

8 

6 

s 

636 

618 

601 

583 

565  J    547 

46 


CHAPTER  V. 

Lintels. 

Some  examples  of  cast  iron  lintels  will  be  found  in 
Chapter  VI.  This  chapter  will  be  taken  up  with  the  sub- 
ject of  steel  lintels. 

Lintels  are  often  made  so  that  only  the  edge  of  a  plate 
or  the  edge  of  an  angle  will  show  in  the  face  of  the 
wall.  The  steel  must  be  set  back  a  little  so  as  to  allow 
pointing  at  the  supports. 


(i) 


Fig.  1  shows  a  number  of  different  styles  of  lintels. 

In  a  solid  wall  it  is  usual  to  calculate  the  lintels  as 
carrying  a  height  of  wall  equal  to  one-third  of  the  opening. 
Where  the  'top  of  a  wall  or  a  large  opening  occurs  a  short 
distance  above  the  lintel,  say  a  height  equal  to  the  span 
or  less,  the  full  height  of  wall  should  be  borne  by  the 
lintel.  If  floor  concentrations  or  wall  piers  occur  over  the 
opening,  the  effect  of  these  loads  must  be  considered. 

A  lintel  such  as  that  shown  at  (a)  Fig.  1,  made  up  of 
2  4"x3"x5-16"  angles  with  the  short  legs  vertical  and  riv- 
eted together,  may  be  used  in  a  9-in.  solid  wall  for  spans 
up  to  8  ft.  Two  6"x3%"x^"  angles  may  be  used  in  like 
manner  in  a  13-in.  wall  for  spans  up  to  8  ft. 

A  standard  9-in.  channel  may  be  used  as  at  (e)  for 
openings  up  to  &/2  ft.,  and  a  standard  12-in.  channel  may 

47 


be  used  for  openings  up  to  71/6  ft.,  'these  in  9-in.  and  13-in. 
walls,  respectively. 

In  the  following  table,  taken  from  "Steel  in  Construc- 
tion" (Pencoid  Iron  Works),  the  lintels  are  selected  to 
deflect  1/360  of  the  span  up  to  10  ft,  and  1/500  of  the 
span  above  15  ft.  The  fiber  stress,  assuming  'the  lintel 
to  carry  a  height  of  wall  Y$  of  the  opening,  is  within 
16,000  Ibs.  per  sq.  in. 

TABLE  I.      ' 

SIZE    OF    STANDARD    I-BEAMS    FOR    LINTELS. 

Span  in   Feet. 
oThWail  8  <>r  9    10  or  11    12  or  13    14  or  15    16  or  17    18  or  20 


9-in.  |  2-4-in. 

2-5-in. 

2-7-in. 

2-8-in. 

2-9-in. 

2-12-in. 

13-in.  |  2-4-in. 

2-6-in. 

2-7  -m. 

2-8-in. 

2-9-in. 

2-12-in. 

18-in.  |  2-5-in. 

2-7  -in. 

2-8-in. 

2-9-in. 

2-10-in. 

2-12-in. 

22-in.  |  2-5-in. 

2-7  -in. 

2-8-in. 

2-9-in. 

2-10-in. 

2-12-in. 

NOTE:     Cast  iron  separators  are  to  be  used  in  every  case. 

Table  I  can  be  used  in  selecting  the  sizes  of  beams  and 
channels  to  be  used  in  lintels,  such  as  those  shown  in  (c) 
and  (d)  Fig.  1,  using  two  channels  in  place  of  a  beam. 
The  angles  should  be  counted  as  simply  acting  as  sup- 
ports for  the  first  few  courses  of  bricks.  The  methods 
given  in  Chapter  VI  may  be  employed  to  find  the  size  of 
beams  and  channels  required  in  any  lintel. 

Sometimes  a  loose  angle  is  used  with  the  lintel,  as  at 
(g)  Fig.  1.  This  is  merely  to  carry  the  face  brick  up  to 
the  level  of  the  top  of  the  beams.  Sometimes  an  I-beam, 
instead  of  the  channel  shown  at  (cl),  is  exposed  in  the 
face  of  the  wall ;  this  allows  building  up  of  the  brick 
work  over  supports,  if  no  offset  occurs  in  the  wall  at 
jambs.  The  wooden  pieces  shown  at  (g),  (h)  and  (i)  are 
for  nailing  on  the  wood  finish.  Separator  bolts  should 
be  ordered  long  enough  to  include  these. 

Separators  for  lintels  are  usually  short  pieces  of  gas 
pipe  slipped  over  the  bolts. 

48 


CHAPTER  VI. 

Beams. 

Beams  may  be  made  of  wood,  cast  iron,  steel  or  rein- 
forced concrete,  though  cast  iron  is  seldom  used  for 
beams,  except  in  the  case  of  window  lintels  and  the  like. 

The  selection  of  wooden  beams  or  joists  to  carry  a 
certain  load  is  restricted,  and  is  also  simplified  by  the 
commercial  sizes.  A  unit  stress  of  800  Ibs.  per  sq.  in. 
should  be  used  for  soft  woods,  such  as  white  pine,  and 
1,000  Ibs.  may  be  used  for  white  oak  and  long-leaf  yel- 
low pine.  A  simple  way  to  find  the  size  of  wooden  beam 
is  by  use  of  Table  I.  In  this  table  the  coefficient  C  is 
equal  to  the  product  of  the  span  of  the  beam  in  feet  and 
the  total  uniform  load  in  pounds,  which  the  beam  can 
safely  carry.  If,  for  example,  a  wooden  beam  of  a  span 
of  10  feet  is  to  carry  a  load  of  150  Ibs.  per  lineal  foot,  or 
1,500  Ibs.,  the  value  of  'the  coefficient  C  for  such  a  beam 
would  need  to  be  10x1,500  or  15,000.  A  2x10  beam  in 
white  pine  or  a  2x9  beam  in  oak  or  yellow  pine  would 
suffice.  The  total  load,  uniformly  distributed,  that  any 
beam  may  safely  carry  is  readily  found  from  the  table  by 
dividing  the  value  C  by  the  span  of  the  beam  in  feet. 
(Note  that  C  is  the  product  of  one-ninth  of  the  unit  stress 
by  the  width  of  beam  by  the  square  of  the  depth.) 

If  the  load  on  a  beam  is  central  and  concentrated,  in- 
stead of  being  uniformly  distributed,  it  should  be  dou- 
bled for  finding  the  size  required,  as  such  a  concentrated 
load  is  twice  as  effective  in  producing  bending  moments 
as  the  same  load  uniformly  distributed.  If,  for  example, 
a  wooden  girder  having  a  span  of  16  feet  is  to  carry  a 
center  load  of  3,500  Ibs.,  the  value  of  C  would  be  2x3,500x 
16=112,000.  A  yellow  pine  beam  4x16  would  suffice. 

The  depth  of  wooden  beams  should  generally  be  be- 
tween one-tenth  and  one-twentieth  of  the  span.  Beams 
deeper  'than  one-tenth  will  be  overstressed  in  shear,  when 


strained  to  their  capacity  in  bending,  with  a  uniform  load; 
beams  shallower  than  about  one-twentieth  will  deflect  too 
much  under  load. 

TABLE  I. 


Size  of  Beam 
in  Inches. 

C,  for  White 
Pine. 

C,  for  Oak 
or  Y.  P. 

2x  4 

2,840 

3,550 

2x  5 

4,440 

5,550 

2x  5 

6,400 

8,000 

2x  8 

11,400 

14,220 

2x  9 

14,400 

18,000 

2x10 

17,800 

22,220 

2x12 

25,600 

32,000 

3x14 

52,270 

65,330 

3x15 

60,000 

75,000 

4x16 

91,020 

113,770 

Cast  Iron  Beams. 

Cast  iron  can  only  be  used  economically  in  beams  in 
shapes  that  have  wide  or  heavy  tension  flanges,  because 
of  -the  weakness  of  cast  iron  in  tension. 


as 


(c) 


fd) 


Lintels  for  brick  walls  are  sometimes  made  in  cast 
iron  in  shapes  such  as  shown  in  Fig.  1.  Calculating  4,000 
Ibs.  per  sq.  in.  tension  on  the  cast  iron,  and  assuming  that 
a  height  of  wall  one-third  the  height  of  the  opening  is 
carried  by  the  lintel,  the  lintel  shown  in  end  view  at  (b) 
could  be  used  in  a  9-in.  brick  wall,  in  ^-in.  metal,  for 
openings  up  to  about  five  feet.  In  ^-in.  metal  it  could  be 
used  for  openings  up  to  six  feet.  The  lintel  shown  in  end 
view  at  (d)  has  just  about  double  the  strength  and  dou- 
ble the  load  of  that  shown  at  (b),  so  that  the  same  limits 


50 


of  spans  can  be  used.  The  one  shown  at  (c)  could  span 
larger  openings,  theoretically,  but  it  is  not  advisable  to 
use  long  beams  in  cast  iron,  because  of  the  uncertainties 
in  the  metal.  Steel  beams  are  more  reliable  for  large 
openings.  Also,  if  the  opening  has  a  pier  or  a  concen- 
trated load  above  it,  steel  lintels  should  be  used,  designed 
to  carry  that  load. 

Steel  Beams. 

Nearly  all  of  the  beams  in  a  building  are  designed  for 
uniform  load,  so  that  the  determination  of  the  sizes  is 
generally  a  simple  matter,  when  tables  are  at  hand.  It 
is  a  common  standard  in  building  work  to  allow  16,000 
Ibs.  per  sq.  in.  extreme  fiber  stress  on  the  steel.  This 
is  a  correct  unit  for  quiescent  loads,  such  as  those  in  build- 
ings. It  would  be  too  high  for  rolling  loads  such  as 
bridges,  so  that  the  methods  and  units  of  this  chapter 
cannot  be  employed  to  design  bridges.  It  should  be  clear- 
ly understood  that  this  chapter,  and  in  fact  this  entire  book, 
applies  only  to  building  work.  Bridges  are  designed  on 
quite  a  different  standard  and  by  different  methods. 

Many  handbooks  give  tables  showing  'the  total  load 
which  a  beam  will  carry.  The  tables  of  this  chapter  give 
instead  a  quantity  for  the  several  sizes  of  beams,  desig- 
nated Q,  by  which  the  capacity  of  a  beam  may  readily 
be  found.  The  quantity  Q  is  equal  to  the  product  of  the 
span  of  a  beam  in  feet  and  the  load  in  tons  (of  2,000 
Ibs.)  that  the  beam  can  safely  carry  as  a  uniformly  dis- 
tributed load. 

To  find  the  size  of  a  beam  for  a  given  case,  it  is  only 
necessary  to  find  the  load  in  tons  that  the  beam  must 
carry  and  multiply  this  by  the  span.  Then  by  looking  in 
the  tables  l?nd  a  value  Q  that  equals  this  product.  That 
beam  is  then  a  proper  size  for  the  case,  assuming  that 
it  is  held  against  lateral  displacement  in  the  building. 

The  full  strength  of  beams,  as  exhibited  in  this  chap- 
ter, is  only  realized  when  the  beams  are  properly  stif- 
fened and  properly  supported  at  the  ends.  For  the  end 
supports  of  beams  see  Chapter  X.  The  matter  of  stiff- 

51 


ening  of  the  beams  or  lateral  support  will  be  considered 
here,  as  this  is  a  matter  vitally  connected  with  the  general 
strength  of  the  beam,  and  it  is  a  matter  not  so  generally 
understood  nor  appreciated  as  that  of  the  necessity  for 
proper  support  at  the  ends  of  a  beam. 

In  Engineering  News,  January  6,  1910,  will  be  found  the 
record  of  an  experiment  on  small  beams  built  of  tin  plate, 
in  which  the  mere  addition  of  end  stiffeners  to  one  of 
two  beams  identically  made  added  129  per  cent  to  the 
ultimate  strength  of  the  beam  thus  stiffened.  The  purpose 
of  adding  the  stiffeners  was  not  to  prevent  the  web  from 
buckling,  but  to  prevent  the  beam  from  keeling  over  at 
the  support.  The  beam  which  had  not  the  end  stiffeners 
failed  by  leaning  of  the  web  in  opposite  directions  at  the 
ends,  or  by  a  twisting  of  the  entire  beam.  This  shows  con- 
clusively, what  analysis  would  dictate,  namely,  that  it 
is  necessary  in  all  beams,  in  order  to  develop  the  full 
strength,  that  the  beam  be  held  against  lateral  tilting  at  the 
ends.  In  the  ordinary  case  in  buildings  this  is  accom- 
plished by  building  the  ends  of  beams  into  the  wall  or  by 
the  riveted  end  connections  of  the  beam. 

The  top  flange  of  a  beam  should  also  be  held  laterally 
at  intermediate  points.  This  is  usually  accomplished  by 
the  arches  between  the  beams  or  the  floor  slabs  resting 
on  top  of  them.  Where  it  is  not  practicable  to  stiffen  the 
compression  flange  of  a  beam  continuously,  it  should  be 
braced  at  intervals.  The  intervals  should  not  be  more 
than  about  sixteen  times  the  width  of  the  flange,  if  the 
full  tabular  value  of  the  beam  is  used.  If  it  is  necessary  to 
have  the  compression  flange  unsupported  for  50  times 
the  width,  only  one-half  of  the  tabular  value  for  the 
strength  of  the  beam  should  be  used.  At  25  times  the 
flange  width,  unsupported,  use  y%  of  the  tabular  load;  at 
33  times,  use  54  '>  at  42  times,  use  ^&. 

When  there  is  any  plastered  work  or  concrete  covering, 
the  depth  of  steel  beam  should  not  be  less  than  about  one- 
twenty-fourth  of  the  span,  so  that  the  deflection  will  not 
be  too  great.  In  other  work  a  limit  of  one-thirtieth  may 
tc"  observed. 

52 


Examples. 

(1)  Given   a  mill   roof   with   channel   purlins   spaced   5 
ft.  apart,  2-inch  matched  tongue-and-groove  board  sheath- 
ing, tar  and  gravel  covering,  snow  load  50  Ibs.  per  sq.  ft., 
span  between  trusses  16  ft.  Assume  7  Ibs.  per  sq.   ft.   for 
covering,  8  Ibs.  per  sq.  ft.  for  sheathing,  and  3  Ibs.  per  sq. 
ft.  for  purlins.     The  load  per  foot  on  purlin  is   (50-}-7-f- 
8-f3)X5=340    Ibs.      The    load    carried    by    one    purlin    is 
340X16=5,440  Ibs.,  or  2.72  tons.     Q  is  then  2.72x16=43.5. 
Q  for  a  standard  8-in.     11 -/4  Ib.  channel  is  43.2,  hence  this 
size  would  be  used. 

(2)  Given  floor  beams   supporting  tile  arches,   span   13 
ft,  distance  apart  6  ft.,  1"  floor  on  sleepers  filled  with  cin- 
der concrete,  live  load  80  Ibs.  per  sq.   ft.     Assume   10-in. 
arches,    which    weigh    39    Ibs.    per    sq.     ft.     The    several 
weights  are:    15   Ibs.    for  cinder  concrete   and   sleepers;,  4 
Ibs.  for  wooden  flooring;  7  Ibs.  for  steel,  fireproofiwg  and 
ceiling,  and  80  Ibs.   for  live  load.     This  is  a  total  of  145 
Ibs.  per  sq.  ft.  or  7.83  tons  per  beam.     Q  is  7.83X18=140.9. 
By  interpolating  between  a  10"  beam  25  Ibs.  and  40  Ibs.,  it 
is  found  that  a  10"  30  Ib.  beam  would  suffice.     If  standard 
beams    are   preferred    12"    31^    Ib.   beams   could   be   used. 
Ten-inch   arches   can   be   used   on   these   by   offsetting  the 
ceiling  at  each  beam.     If  conditions  permitted,  closer  spac- 
ing of  the  beams  could  be  used,  and  10-in.  25  Ib.  I-beams 
would  suffice. 

(3)  Given  floor  beams  spaced  9  ft.  apart  supporting  a 
4-inch   reinforced  concrete   slab   with    1-inch  tile  floor   on 
the  same,  the  span  being  20  ft,  and  live  load  100  Ibs.  per 
sq.   ft.  The  load  per  sq.   ft.  is  as   follows:   Live  load   100, 
concrete  50,  tile  and  filling  20.    This  is  1,530  Ibs.  per  lineal 
foot  of  beam.     Adding  for  weight  of  beam  and  surround- 
ing concrete   150  Ibs.  per   ft.,   the  weight  on  the  beam   is 
1,680X20=33,600,  or   16.8  tons.     Q   is  336.     By  interpola- 
tion a  15"  50-lb.  beam  is  found  to  be  correct. 

(4)  Given  a  double  wall  beam  to  be  made  up  of  an  I-- 
beam and  a  channel  of  the  same  depth,  the  beam  to  carry 
12  ft.  of  vertical  height  of  a  13-inch  wall  and  4  ft.  of  a 

53 


floor  load  at  200  Ibs.  per  sq.  ft.  total,  the  span  being  18 
ft.  The  wall  will  weigh  130X12  or  1,560  Ibs.  per  lin.  ft. 
Adding  to  this  800  Ibs.  for  the  floor  load  and  60  Ibs.  for 
the  weight  of  the  beam,  we  have  2,420  Ibs.  per  lineal  foot. 
The  load  carried  by  the  beam  is  then  21.78  tons,  and  Q  is 
392.  By  trial  it  is  seen  that  a  12"  I  40  Ibs.  and  a  12"  chan- 
nel 35  Ibs.  will  have  a  combined  value  of  Q  equal  to  this. 
By  using  a  channel  and  beam  of  different  depths  stand- 
ard sections  could  be  employed,  as  a  15"  beam  42  Ibs.  and 
a  12"  channel  20.5  Ibs. 

(5)  Given    a    system    of    T    bars,    supporting    18-inch 
book  tiles,  carried  on  purlins  spaced  10  ft.  apart.    Weight 
of  book  tile   arid  roofing  per  sq.   ft.  30  Ibs.,   live  load  50 
Ibs.   Total   weight  on   T  bar  80x1^X10=1,200=0.6  ton. 
Q=6.     A  3X3X10.1  Ib.  T  would  suffice. 

(6)  Given  a  system  of  double  angles  spaced  4  ft.  apart 
on  a  span  of  8  ft.  supporting  a  balcony ;  live  load  60  Ibs. 
per  sq.  ft.    Assume  a  slab  weight  of  50  Ibs.  per  sq.  ft.  total. 
A   pair   of   angles    will   carry    110x4x8=3,520    Ibs    or    1.76 
tons.     Q=1.76x8=14.08.     The   value   of    Q    for   2   angles 
4"x3"x->£,  long  legs  vertical,  is  15.6.     Note  that  these  angles 
would  weigh  more  than  beams  or  channels   of  the   same 
strength,  and  they  would  hence  not  be  the  most  economical 
section  to  use.     However,  they  afford  a  better  seat  for  a 
slab,   if   it   is   the    intention    to   keep   the  supporting   beam 
within  the  depth  of  the  slab.     Xote  that  a  4x5x1 5.7-lb.  T- 
bar  would  be  of  sufficient  strength   for  this  case,  but  the 
5-inch  stem  might  be  too  deep. 


WJ  M  = 

Fig.  2. 

54 


M  .  wi 


In  Fig.  2  are  given  several  cases  of  beams  and  the 
bending  moments  for  each.  Case  1  is  that  of  a  simple 
beam  uniformly  loaded.  The  values  of  Q  in  Tables  II  to 
VII  are  for  this  case.  They  can  be  made  to  apply  to  any 
of  'the  other  cases  as  follows: 

For  a  single  concentrated  load  at  the  center  of  a  given 
span  it  is  seen  that  the  bending  moment  M  is  just  double 
that  which  the  same  load  would  produce  if  uniformly  dis- 
tributed over  the  span.  Hence  a  single  concentration  at 
the  center  of  a  span  will  give  the  same  bending  as  twice 
that  load  uniformly  distributed.  To  use  Tables  II  to  VII, 
then,  we  will  have  to  double  the  concentration  and  use 
that  load  as  a  uniform  load. 

Examples : 

(1)  Given    an    I-beam    on    a    12-ft.    span    supporting   a 
concentrated    load    at    the    center    of    span    of    24,000    Ibs. 
Doubling   this    to    find    the    equivalent    uniform    load    and 
multiplying  by   12    (after   reducing  to  tons)    we   have  288 
as  the  value   of   Q,   A   15" -I,   42  Ibs.   would   then  be   re- 
quired. 

(2)  Given  a  pair  of  beams  on  a  span  of  8  ft.  support- 
ing a  column  load   at  the  center  of   span   of    150,000  Ibs. 
150,000X2=300,000   Ibs.   or    150   tons.      150x8=1,200,   the 
value  of  Q.    Two  20"  beams  65  Ibs.  have  a  value  Q=l,248. 

(3)  Given  an  opening  in  an  18-in.  wall  17  ft.  wide  and 
a  floor-girder  just  above  the  middle  of  same  with  a  load 
of  37,500  Ibs.    Call  the  span  of  the  lintel  18  ft.  wide  and  as 
sume   a   wall   load  6   ft.    high   or    180X6X18=19,440  Ibs. 
The    equivalent  uniform   load   is   37,500X2+19,440=94,440 
Ibs.  or  47.22  tons.     Q  is  47.22x18=850.   .Two  18"  beams 
55  Ibs.  would  be  somewhat  stronger  than  necessary. 

When  the  concentrated  load  is  not  at  the  center  of  span, 
a  special  case  arises,  and  the  simplified  methods  of  this 
chapter  do  not  apply. 

Case  3  in  Fig.  2  is  for  a  cantilever  beam  uniformly 
loaded.  It  is  seen  that  the  bending  moment  is  four  times 
as  great  for  the  same  load  and  span  as  that  found  in  a 

55 


simple  beam.  Hence  the  equivalent  load  for  a  simple  span 
to  be  used  in  tables  II  to  VII  will  be  four  times  the  actual 
uniform  load  on  the  span. 

Examples : 

(1)  Given  a  roof  truss  load  of  80,000  Ibs.  to  be  distrib- 
uted by  means  of  two  wall  beams  5  ft.  long  into  a  brick 
wall. 

.  25'  1  2.5 


mtmmt 

BO ooo LSV 

Fig  .3. 

Here  the  load  which  is  uniformly  distributed  is  an  up- 
ward one,  being  the  reaction  of  the  brick  wall  against  the 
beams.  The  span  /  is  2.5  ft.  and  the  load  on  each  of  these 
cantilevers  is  40,000  Ibs.  The  equivalent  load  for  a  simple 
beam  is  4X40,000=160,000  Ibs.  or  80  tons.  Q  is  80x2^= 
200.  Two  9"  beams  21  Ibs.  have  a  value  of  Q  equal  to 
201.6. 

(2)  Given  a  building  in  which  the  wall   is  omitted  at 
the  corner  for  a  distance  of  6  feet,  there  being  no  corner 
post  but  cantilever  beams  at  the  second  story  meeting  at 
the  corner  and  supporting  the  wall  and  floors  above.  As- 
sume that  the  total  weight  of  wall  and  floor  load  is  4,200 
Ibs.  per  running  foot,  and  that  the  effectual  span  of  the 
cantilever  is  7  ft.     The  load  carried  by  the  cantilever  is 
4,200X^=29,400   Ibs.     The   equivalent    load    for    a    simple 
span  is  29,400X4=117,600  Ibs.  or  58.8  tons.  Q  is  58.8x7= 
411.6.    Two  12-in.  35-lb.  beams  would  come  within  a  small 
percentage  of  filling  the  requirements. 

(3)  Given  roof  rafters  projecting  4  ft.  beyond  a  wall 
and  supporting  rienforced  concrete   slabs,   the  rafters  be- 
ing spaced  6   ft.   and  the  total  load  carried  being  80  Ibs. 
per    horizontal    square    foot.      The    load    on    a    rafter    is 
80X4X6=1,920    Ibs.      The    equivalent    load    for    a    simple 
beam   is    1,920X4=7,680=3.84  tons.     Q   is   3.84X4=15.36. 

56 


The  rafter  could  be  a  4"  7,^-lb.  beam,  or  a  5"  6^-lb. 
channel,  or  a  2-4"X3"X^s"  angles,  or  a  4"X/4"  zee-bar, 
or  a  4"x5"Xl6.7-lb.  T-bar. 

Case  4  in  Fig.  2  is  for  a  concentrated  load  at  the  end  of 
a  cantilever.  The  moment  here  is  eight  times  as  great 
for  a  given  span  and  load  as  that  for  a  simple  beam.  The 
equivalent  load  for  a  simple  beam  is  then  eight  times  the 
amount  of  the  concentration. 

Examples. 

(1)  Given  a  balcony  7  ft.  wide  supported  on  cantilever 
beams  spaced   12   ft.   apart.     A    facia  beam   supports   one 
side  of  a  slab  and  a  railing.     Assume  the  floor  load  on 
the  facia  beam  to  be  420  Ibs.  per  ft.,  and  the  railing  to 
weigh  40  Ibs.  per  ft.     The  concentrated  load  at  the  end  of 
the  cantilever  beam  is  then  460X12=5,520  Ibs.  or  2.76  tons. 
The  equivalent  uniform  load  for  a  simple  span  is  2.76X8= 
22.08.    Q  is  22.08X7=154.56.    This  could  be  a  10"-I  35  Ibs. 
or  2-10"  channels  20  Ibs. 

(2)  Given   a   cantilever   beam   supporting   a  column   at 
its  end,  the  overhang  being  4  ft  and  the  column  load  being 
120,000   Ibs.     The    equivalent    load    for   a   simple   beam   is 
120,000X8=960,000,  or  480  tons.    Q  is  480x4=1,920.    This 
would  require  2-24"  I  beams  85  Ibs. 

(3)  Given  a  cantilever  beam  supporting  a  uniform  load 
of  800  Ibs.  per   ft.  and  a  concentrated  load  at  the  outer 
end  of   10,000  Ibs.,  'the  span  being  10   ft.     The  equivalent 
uniform  load  for  a  simple  beam  is  8,000  (the  total  uniform 
load)  x  4+10,000X8  or  112,000  lbs.=56  tons.    Q  is  56x10 
=560.    A  15"  I  80  Ibs.  would  do,  but  a  20"  I  65  Ibs.  is  much 
stronger  and  would  weigh  less. 


57 


TABLE   II. 

Capacity  of  Standard  I  Beams  and  Channels 
Extreme  fiber  stress  16,000  Ibs.  per  sq.  in. 


Size. 

Q. 

Size. 

0- 

Size. 

Q. 

24"         100       Ib. 

1058.2 

/  10"  I      40       Ib. 

|    169.1 

j  12"   Ch.  40        Ib. 

174 

24"          80       Ib. 

928.0 

X  10"  I      25       Ib. 

130.1 

1  12"  Ch.  20>4  Ib. 

114 

20"        100       Ib. 

883.2 

j    9"  I      35       Ib. 

132.3 

/  10"  Ch.  35       Ib. 

123 

20"          80       Ib. 

782.4 

J    9"  I      21       Ib. 

100.8 

\  10"  Ch.  15       Ib. 

71 

20"          75       Ib. 

676.9 

j    8"  I      25  54   Ib. 

91.2 

f    9"  Ch.  25       Ib. 

83. 

20"          65       Ib. 

624.0 

j    8"  I      18      Ib. 

75.7 

1    9"   Ch.  1354   Ib. 

56. 

18"          70       Ib. 

546.1 

)    7"         20       Ib. 

64.5 

j     8"  Ch.  2154   Ib. 

63. 

18"          55       Ib. 

471.6 

}    7"          15       Ib. 

55.5 

<     8"  Ch.  1  1  54   Ib. 

43. 

/  15"        100       Ib. 

640.6 

/    6"          1754  Ib. 

46.4 

(     7"  Ch.  19^4   Ib. 

50 

1  15"          80       Ib. 

565.9 

\    6"          1*54  Ib. 

38.9 

1     7"  Ch.    9)4   Ib. 

32 

/  15"          75       Ib. 

491.7 

/    5"          14y4  Ib. 

32.5 

/    6"  Ch.  1554  Ib. 

34. 

115"          60       Ib. 

433.0 

15"            9M  Ib. 

25.6 

1    6"  Ch.    8       Ib. 

22. 

{15"          55       Ib. 

363.2 

J    4"          1054  Ib. 

19.2 

J     5"  Ch.  1154  Ib. 

22 

115"          42       Ib. 

I    314.  T 

1    4"             754  Ib. 

16.0 

1     5"  Ch.    654  Ib. 

16. 

f  12"          55       Ib. 

285.3 

J    3"            754  Ib. 

10.1 

/    4"  Ch.    754   Ib. 

12 

1  12"          40       Ib. 

238.9 

13"           554  Ib. 

9.1 

\     4"  Ch.    554  Ib. 

10 

M2"          35       Ib. 

202.7 

f  15"  Ch.  55       Ib. 

306.1 

j     3"  Ch.    6       Ib. 

7 

1  '2"          3154  Ib. 

192.0 

1  15"  Ch.  33       Ib. 

222.4 

1      3"  Ch.    4       Ib. 

5 

NOTE;— It  is  preferable  to  use  the  lighter  or  standard 
weight  of  the  several  bracketed  pairs.  For  intermediate  weigkti 
interpolate  to  find  the  value  of  Q. 


TABLE   III. 

Capacity  of  Bethlehem  I  Beams* 
Extreme  fiber  stress  16.000  Ibs.  per  sq«  in. 


Size.                    Q. 

Size. 

Q. 

Size. 

1     Q. 

30"       120       Ib.  |1862.  9 

20"   I     59        lb.|    625.1 

15"   1      38       Ib. 

314. 

28"       105       Ib. 

1529.1 

18"  I     59       Ib. 

523.2 

12"  I      36       Ib. 

239. 

26"         90       Ib. 

1221.3 

18"  I     54       Ib. 

499.2 

12"  I     32       Ib. 

203. 

24"         84       Ib. 

1058.7 

18"  I     52       Ib. 

489.1 

12"  I     2854   Ib. 

192. 

24"         83       lb.|   995.7 

18"  I     4854   Ib.i   473.1 

10"  I     2854   Ib. 

143. 

24"         73       lb.|   929.6 

15"  I     71       Ib. 

566.4 

10"  I     2354   Ib. 

131. 

20"         82       li). 

832.  Oj 

15"  I     64       Ib. 

472.5 

9"  I     24       Ib. 

109. 

20"         72       Ib. 

782.4 

15"  I     54       Ib. 

433.6 

9"  I     20       Ib. 

100. 

20"     -  69       Ib. 

676.  81 

15"  I     46       Ib. 

344.5 

8"  I     1954   Ib. 

80. 

20"  I     64       Ib. 

651  .7 

15"   I     41        Ib.i    324.8 

8"   T      WV*   Ib. 

76. 

58 


TABLE   IV. 


Capacity  of  Bethlehem  Girder  Beams* 
Extreme   fiber  stress  16,000  Ibs.  per  sq.  in. 


Size.      |  Q. 

Size.      |  Q. 

Size.     |  Q. 

30"  200   lt>. 
30"  180   Ib. 
28"  180   Ib. 
28"  165   Ib. 
26"  160   Ib. 
26"  150   Ib. 
24"  140   Ib. 

3253.3 
2913.6 
2767.5 
2500.3 
2306.1 
2114.7 
1867.2 

24"  120   Ib. 
20"  140   Ib. 
20"  112   Ib. 
18"  92   Ib. 
15"  140   Ib. 
15"  104   Ib. 
15"  73   Ib. 

1603.2 
11565.3 
1249.1 
942.9 
1132.8 
867.7 
628.3 

12"  70   Ib. 
12"  55   Ib. 
10"  44   Ib. 
9"  38   Ib. 
8"  32  H  Ib. 

478.9 
384.0 
260.3 
202.7 
152.5 

TABLE    V. 
CAPACITY  OF  ANGLES  IN  BENDING. 

Long  Leg  Vertical,  for  Unequal  Leg 
olngles. 

Extreme  fiber  stress  16,000  Ibs.  per  sq.  in. 


Size.           |      Q. 

Size.           |      Q. 

Size.           | 

Q. 

8     x8     xl 

84.3 

2j4x2J4x   l/2\      3.9 

5     x3     x  ft 

18.9 

8     x8     x  y2 

44.6 

2^x2^x  y4 

2.1 

5     x3     x  A| 

10.1 

6     x6     x  y4 

35.5 

2     x2     x  ft 

1.9 

4     x3     x  ft 

12.3 

6     x6     A  3/8 

18.8 

2     x2     x  T3ff 

1.0 

4     x3     x  ft| 

6.6 

5     x5     x  Y4 

24.2 

7     x3^x  ft\   43.8 

3Hx3     x  ft 

9.4 

5     x5     x  ft 

12.9 

7     x3^x  fe\   26.7 

3^x3     x  M 

5.1 

4     x4     x  Y4 

15.0 

6     x4     x  Y4 

33.3 

3^x2^x   y2 

7.5 

4     x4     x  TB8 

6.9 

6     x4     x  ft 

17.7 

3^x2^x   y4 

4.0 

3y2x3y2x  ft 

9.7 

6     x3y2x  ft 

32.5 

3     x2^x   ya 

5.6 

3^x3^x  A| 

5.2 

6     x3y2x  ft 

17.3 

3     x2^x   y4 

3.0 

3     x3     x   y2 

5.7 

5     x3^x  ft 

22.8 

2y2x2     x  ft 

2.9 

3     x3     x   y4 

3.1 

5     x3J/2x  T5ff 

10.3 

2^x2     x  A| 

1.6 

NOTE  —  Interpolate    for    intermediate    thicknesses. 

59 


TABLE   VI. 

Capacity  of  Zee-Bars  in  Bending. 
Extreme  fiber  stress  16,000  Ibs.  per  sq.  in. 


Size. 

Q. 

Size.           |     Q. 

Size. 

Q. 

6     x3l/2x  Ml   45.0 

5     x3J4x  y2\   41.0 

4     x3Jsx  5^ 

32.3 

Al    52.4 

Al   46.0 

H 

35.5 

59.9 

H\   51.0 

M 

38.7 

6     x3j^x  T9g 

61.4 

5     x3y4x  HI   50.5 

3     x2H*   54 

10.2 

H 

68.4 

?4 

55.2 

A|    12.7 

H 

75.2 

if 

59.7 

3     x2Hx  Ml    13.7 

74.9 

4     x3Ax   H 

16.8 

Al    15.9 

x  }i 

81.2 

A 

20.9 

3     x2}Jx   y.\   16.3 

87.5 

24.9 

9 

18.3 

5     x3J^x  isg 

28.5 

4     xS-i^x  A 

25.8 

H 

34.1 

HI   29.3 

A 

39.7 

T9*l    33.0 

NOTFy    —    Web,    flange    and    thickness    increase    by     same 
amount  in  each  group. 


TABLE    VII. 

Capacity  of  Carnegie  Tee- Bars  in  Bending. 
Extreme  fiber  stress  16,000  Ibs.  per  sq.  in. 


Size,  Flange 
by  Stem  by 
Wt.  per  Ft. 

Q. 

Size,  Flange 
by  Stem  by 
Wt.  per  Ft. 

Q. 

Size,  Flange 
by  Stem  by 
Wt.  per  Ft. 

Q- 

5     x3     x!3.6|     6.3 

3^x4     xlO.O 

8.3 

2>4x3     x  7.2 

4.6 

5     x2^xll.O 

4.6 

3^x3^x11.9 

8.1 

2j^x3     x  6.2 

4.1 

4^x3^x15.9 

11.4 

3Hx3^x  9.3 

6.4 

2^x2^x  6.8 

3.9 

4J/2X3     x  8.6 

4.3 

3^x3     xll.O 

6.0 

2^x2^x  5.9 

3.2 

4j4x3     xlO.O 

5.0 

3^x3     x  8.7 

4.7    . 

2^x2^x  6.5 

3.1 

4y2x2y2x  8:0 

3.0 

3^x3     x  7.7 

3.8 

2^x2^x5.6       2.7 

4*/2x2y2x  9.3 

3.5 

3     x4     xll.9 

10.3 

2^x1  J4x  3.0 

0.5 

4     x5     x!5.7 

16.5 

3     x4     xlO.6 

9.5 

2y4x2y4x  5.0 

2.2 

4     x5     x!2.3 

13.0 

3     x4     x  9.3 

8.4 

2%x2y4x  4.2 

1.7 

4     x4^x!4.8 

13.6 

3     x3^xll.O 

7.9 

2     x2     x  4.4 

1.8 

4     x4^xll.6 

10.6 

3     x3j^x  9.8 

7.3 

2     x2     x  3.7 

1.3 

4     x4     x!3.9 

10.8 

3     x3^x  8.6 

6.5 

2     xl^x  3.2 

0.8 

4     x4     xlO.9 

8.7 

3     x3     xlO.l 

5.9 

\Mxiy4x  3.2 

1.0 

4     x3     x  9.3 

4.7 

3     x3     x  9.0 

5.4 

l^xl^x  2.6 

0.7 

4     x2^x  8.7 

3.3 

3     x3     x  7.9 

4.6 

iy2xiy2x  2.0 

0.6 

4     x2^x  7.4 

2.9 

3     x3     x  6.8 

3.9 

iiAxiy4x  2.1 

0.5 

4     x2     x  7.9 

2.1 

3     x2^x  7.2 

3.2 

\y4x\y4x  1.7 

0.4 

4     x2     x  6.7 

1.8 

3     x2^x  6.2 

2.8 

1     xl     x  1.3 

0.3 

3^x4     x!2.8 

10.6 

2^x2     x  7.4 

4.0 

1      xl      x   1.0 

0.2 

60 


Reinforced  Concrete  Beams. 

In  the  author's  book  "Concrete"  a  simple  theoretic  treat- 
ment of  reinforced  concrete  beams  is  given;  also  certain 
rules  are  derived  for  the  design  of  such  beams.  The 
reader  is  referred  to  that  book  for  a  discussion  of  the 
theory ;  the  rules  will  be  summarized  here  and  a  brief  out- 
line of  the  theory  given. 

The  generally  accepted  standard  of  reinforced  concrete 
design  in  America  is  a  hodge-podge  of  so-called  practical 
mens'  patented  ideas,  given  a  semblance  of  authority  by 
eminent  investigators  and  authors,  who  discuss  designs 
and  tests  with  little  or  no  logical  analysis  of  the  stresses 
in  the  reinforcement.  Sharp  bends  are  made  in  rods,  loose 
stirrups  are  assigned  stresses  that  they  could  not  possibly 
take,  steel  rods  are  crowded  into  the  stem  of  T-beams 
with  no  regard  to  the  ability  of  the  concrete  to  transmit 
stress  into  the  steel — these  and  many  other  absurdities 
stamp  present  day  practice  in  reinforced  concrete  as  be- 
ing on  a  far  lower  plane  than  highway  bridge  design  of 
20  years  ago.  The  light  highway  bridges  ofc  the  early  days 
of  steel  bridge  are  gradually  being  condemned  or  fail- 
ing, not  because  of  wear  but  because  of  original  weakness; 
many  large  reinforced  concrete  buildings  have  already 
failed,  at  the  time  when  they  were  nearly  completed,  be- 
cause of  weak  design. 

Reinforced  concrete  is  a  most  excellent  form  of  con- 
struction, when  properly  designed,  but  American  standard 
design,  as  exhibited  in  nearly  all  the  books  and  in  the 
greater  part  of  the  work  as  illustrated  in  engineering  peri- 
odicals, is  far  from  being  on  a  sound  basis. 

In  a  paper  entitled,  "Some  Mooted  Questions  in  Rein- 
forced Concrete  Design,"  by  the  author,  read  before  the 
American  Society  of  Civil  Engineers  in  March,  1910,  com- 
mon practice  in  reinforced  concrete  design  is  severely  criti- 
cised in  sixteen  indictments  covering  as  many  phases  of 
that  practice.  The  wide  publicity  given  this  paper,  (it  was 
reprinted  in  Engineering  News  and  very  fully  reviewed  in 
Concrete  Engineering),  puts  it  beyond  peradventure  that 

61 


all  of  the  authors  and  investigators  whose  methods  of 
design  and  analysis  were  attacked  in  that  paper  are  aware 
of  the  attack.  Very  few  have  made  any  defense  of  any 
sort.  The  criticism  which  followed  the  reading  of  the 
paper,  by  its  illogical  analysis,  dogmatic  assertions  and 
dodging  arguments,  as  well  as  the  strong  support  given 
by  many  eminent  engineers,  has  served  to  strengthen  the 
stand  taken  by  the  author;  it  proves  the  crying  need  of 
reform  in  reinforced  concrete  design. 

The  foregoing  is  deemed  to  have  proper  place  in  this 
book  because  the  book  is  designed  for  a  class  of  men  who 
have  to  deal  with  buildings,  and  because  it  is  in  building 
work  that  the  greatest  faults  in  design  are  exhibited ;  it  is 
in  building  work  too  that  the  greatest  wrecks  have  oc- 
curred. 

The  author's  castigation  of  common  practice,  both  in 
reinforced  concrete  and  in  steel  design,  (See  "Engineer- 
ing News,"  April  11,  1907)  has  no  other  motive  than  a 
desire  to  do  what  he  can  to  place  structural  design  of  all 
kinds  on  a  sound  engineering  basis. 

Following  are  a  number  of  rules  of  design  for  beams  in 
reinforced  concrete. 

Rule  1.  Use  no  loose  stirrups.  They  interfere  with  the 
pouring  of  the  concrete ;  they  cannot  possibly  take  any 
kind  of  stress  commensurate  with  their  size ;  they  are  prac- 
tically useless  until  failure  has  begun  in  the  beam  and  are 
therefore  illogical  as  an  element  of  design.  Figs.  4  and  5 
show  how  beams  with  stirrups  may  fail.  The  upper  loose 
ends  may  readily  pull  out  of  the  concrete. 


r 


\fL 


62 


Rule  2.  Make  no  sharp  bends  in  reinforcing  rods  where 
any  considerable  stress  in  the  rods  exists.  At  the  bend 
there  is  set  up  a  side  stress  in  the  concrete  which  the  lat- 
ter is  unable  to  resist.  Rods  should  be  given  gentle  curves, 
preferably  with  a  radius  equal  to  20  times  the  diameter  of 
the  rod. 

Rule  3.  Place  no  dependence  upon  hooks  or  sharp  bends 
in  rods  as  anchors.  Anchorage  of  steel  rods  may  be  erf- 
fected  by  embedment  in  concrete  to  a  depth  of  50  times 
the  diameter  of  the  rod  beyond  the  point  where  the  full 
strength  of  the  rod  is  needed;,  or  it  may  be  effected  in  a 
round  rod  by  use  of  an  end  nut  and  a  washer  or  bearing 
plate,  the  latter  having  a  bearing  surface  about  twenty 
times  the  area  of  the  rod. 

Rule  4.  Reinforcing  rods  at  the  bottom  of  a  reinforced 
concrete  beam  extending  straight  from  end  to  end  of  span, 
should  have  a  diameter  not  more  than  1-200  of  the  length 
of  span. 

Rule  5.  Reinforcing  rods,  when  curved  up  to  the  top  of 
a  beam,  should  run  to  the  end  of  span  and  be  anchored 
over  the  support  or  run  beyond  the  support  so  as  to  take  a 
hold  in  the  concrete.  The  practice  of  bending  up  rods 
with  a  sarp  bend  and  of  ending  them  short  of  the  sup- 
port, or  even  at  the  support,  and  not  anchoring  them  over 
or  beyond  the  support,  is  a  poor  and  illogical  one. 

Rule  6.  In  beams  having  a  depth  of  about  one-tenth  of 
the  span  or  more,  shear  reinforcement  is  needed.  Some 
of  the  reinforcing  rods  should  be  curved  up  as  shown  in- 
Figs.  6,  7,  8,  9. 


63 


Note  that  50  diameters  of  the  rod  is  allowed  beyond  the 
edge  of  support  for  anchorage  in  Fig.  6,  7,  and  8.  In  Fig. 
9  washer  plates  and  nuts  are  used.  If  the  width  of  a 
beam  resting  on  a  wall  is  sufficient,  the  rod  may  be  curved 
down,  as  in  Fig.  7,  and  receive  sufficient  anchorage  within 
the  confines  of  the  beam.  The  curve  should  not  be  sharp 
but  with  a  radius  of  about  20  times  the  diameter  of  the 
rod.  In  a  continuous  line  of  beams  the  portion  of  the  rod 
that  extends  into  the  next  beam  for  anchorage  may  per- 
form the  additional  service  of  acting  as  upper  reinforce- 
ment in  that  'beam.  Continuity  of  beams  will  of  course 
give  rise  to  tension  over  the  suports  at  the  top  of  the 
beams.  Some  of  the  rods  may  be  bent  as  shown  in  Fig. 
8  (all  of  these  should  run  into  the  next  beam  for  full  an- 
chorage), but  there  is  scarcely  any  need  of  this;  they  could 
all  be  bent  as  in  Fig.  6,  as  any  local  irregularities  in  the 
shear  can  readily  be  taken  care  of  in  the  concrete. 

Rule  7.  The  width  of  a  beam  should  be  about  equal  to 
the  sum  of  the  perimeters  of  all  reinforcing  rods  that  lie 
near  the  bottom  of  the  beam  from  end  to  end  of  span. 
This  rule  would  make  the  spacing  of  square  rods  four 
times  their  diameters  and  of  round  rods  3.14  times  their 
diameters,  with  a  side  distance  of  2  and  1.57  diameters 
respectively  on  each  side  of  the  outer  rods.  Several  tiers 
of  rods  in  the  bottom  of  a  beam  should,  in  general,  be 
avoided. 

In  addition  to  the  foregoing  rules  for  the  design  of 
individual  beams  it  is  important  to  add  these  two  pre- 
cautions :  First,  in  the  general  design  the  entire  structure 
should  be  tied  together  so  as  to  preserve  its  integrity. 
Beams  should  be  joined  to  one  another  by  rods;  they 
should  be  tied  into  the  columns;  slabs  should  be  tied  into 
the  beams  and  girders.  Second,  where  beams  or  girders 
frame  end  to  end,  there  should  be  reinforcing  rods  near 
the  top  running  across  the  support  to  prevent  cracking. 
It  is  recommended  that  the  area  of  this  reinforcing  steel 
across  the  supports  be  equal  to  one-half  of  that  of  the 
reinforcement  of  the  beams  at  middle  of  span,  also  that 

64 


the  rods  reach  from  quarter-sp£$  to  quarter-span  of  the 
beams. 

The  following  unit  stresses  are  recommended : 

Tension  on  steel,  14,000  Ibs.  per  sq.  in. 

Compression  on  extereme  fiber  of  the  concrete,  600  Ibs. 
per  sq.  in. 

Shear  on  gross  section  of  concrete  about  30  Ibs.  per 
sq.  in. 

Tables  VIII  to  XIII  give  reinforcement  and  sizes  of 
rectangle  of  concrete,  as  well  as  a  coefficient  to  determine 
the  carrying  capacity,  of  beams  designed  according  to  the 
foregoing  rules  and  with  the  unit  stresses  just  given. 

In  all  of  these  tables 

b  is  the  width  of  concrete  beam; 

d  is  the  depth  out  to  out  of  the  concrete  beam. 

The  center  of  the  reinforcing  rods,  at  middle  of  span, 
is  one-eighth  of  the  depth  d  from  the  bottom  of  the  beam. 
This  makes  the  depth  of  concrete  protecting  and  gripping 
the  steel  proportional  to  the  magnitude  of  the  rod,  as  it 
should  be. 

The  neutral  axis  of  the  beam  is  in  all  cases  assumed 
to  be  at  the  middle  of  the  depth  of  the  concrete  beam. 

Tables  VIII  and  IX  are  for  a  single  straight  rod.  (Of 
course  several  rods  may  be  used  by  making  the  width  in 
multiples  of  b.}  In  these  tables  as  in  the  others,  the  steel 
area  is  1.07  per  cent.  This  governs  the  area  of  beam  or 
the  product  of  b  and  d.  The  minimum  value  of  b  is  the 
perimeter  of  a  rod.  The  minimum  value  of  the  span 
length  is  governed  first  by  200  times  the  diameter  of  the 
rod  and  second  by  twelve  times  the  depth.  The  first  is 
in  accordance  with  Rule  4;  the  second  is  to  keep  the  beam 
well  within  Rule  6,  since  it  has  no  shear  reinforcement. 

Tables  X  and  XI  are  for  reinforcement  with  three 
rods,  two  of  which  are  straight,  and  the  third  is  curved  up 
as  illustrated  in  Figs.  6,  7,  and  9.  The  last  mentioned  rod 
carries  the  shear  which  the  concrete  is  not  capable  of  tak- 
ing. This  rod,  being  curved  up  in  an  approximate  para- 
bolic shape,  will  take  the  shear  incident  to  its  own  stress, 

65 


or  one-third  of  the  total.  The  remainder  of  the  shear 
is  carried  by  the  concrete.  This  condition  governs  the 
minimum  span  length.  Another  governing  condition  in  the 
minimum  span  length  is  200  times  the  diameter  of  rods. 
It  is  seen  that  the  width  of  beam  is  nowhere  less  than 
the  sum  of  the  perimeters  of  the  two  straight  rods.  It 
will  also  be  seen  that  the  depths  all  lie  between  23  and  36 
times  the  diameter  of  the  rods.  This,  however,  has  no 
special  significance. 

Tables  XI  and  XII  are  for  reinforcement  with  four 
rods,  two  of  which  are  straight  and  the  other  two  are 
curved  up  as  illustrated  in  Figs.  6,  7  and  9.  The  two  curv- 
ed rods  carry  one-half  the  shear  and  the  concrete  carries 
the  other  half.  This  condition  governs  the  minimum  span 
length,  which  is  further  limited  by  200  times  the  diameter 
of  rods.  The  width  of  the  beam  is  nowhere  less  than  2Vz 
times  the  perimeter  of  one  rod.  The  depths  all  lie  between 
29  and  38  diameters. 

Examples. 

(1)  Given  a  9-in.  wall  spanning  a  6-ft.  opening,  5  ft. 
of  wall  above  the  opening.    Required  a  reinforced  concrete 
lintel  to  carry  the  wall  and  1,000  Ibs.  per  ft.  of  floor  load. 
The  weight  of  the  wall  is  90X5X6=2,700  Ibs.,   and   the 
floor  load  is  6,000  Ibs.     C=8,700X6.5=56,600.   (Note  that 
6.5   ft.  is  used  as  the  span  to  allow   for  bearing  on  the 
wall.      By  reference  to  Table  VIII  it  is  seen  that  4  beams 
2^4"  wide  and  10^"  deep,  with  four  y2"  square  rods  for 
reinforcement,   would   have   a  value    C— 69,400.     This    is 
more  than  necessary.     The  lintel  would,  of  course,  be  9" 
wide  and  Wl/2"  deep  with  four  W  square  rods  lying  near 
the  bottom.      It  is  assumed  that  the  depth  of  lintel  is  in- 
cluded in  the  height  of  wall,  so  that  no  extra  allowance 
was  made  for  the  weight  of  the  lintel.     The  Ikitel  should 
rest  on  the  wall   for  about   10"  at  each  end.     The   rods 
would  be  about  7l/2  feet  long. 

(2)  It  is  desired  to  design  a  ribbed  floor  filled  with  12" 
t'le,    the    reinforced    concrete    ribs    being    about   4"    wide. 
Span,  16  ft.     Over  the  ribs  will  be  laid  wooden  sleepers, 


filled  in  between  with  cinder  concrete ;  on  the  sleepers 
will  be  nailed  a  1"  maple  floor.  Live  load  66  Ibs.  per  sq, 
ft.  Each  rib  supports  16"  of  floor.  The  weights  per  foot 
are:  Live  load,  88;  tile,  44;  rib  (estimated),  50;  cinder 
fill  and  sleepers,  30;  flooring,  5.  Total,  217  Ibs.  per  ft. 
Total  load  on  one  rib=21 7X16=3,472  Ibs.  C=3,472X 
16=55,550.  By  reference  'to  Table  VIII  it  is  seen  that  a 
324"X14"  rib  with  one  24"  square  rod  for  reinforce- 
ment has  a  value  C=52,100,  which  is  sufficiently  close 
to  the  requirements. 

(3)  Required  a  reinforced  concrete  beam  carrying  a 
floor  load  of  800  Ibs.  per  ft.  on  a  clear  span  of  16  ft.  The 
assumed  weight  of  the  beam  is  180  Ibs.  per  ft.  Total  load 
on  beam  980X16=17,480  Ibs.  0=17,480X16=279,700.  Ap- 
plying tables  VIII  to  XIII  inclusive  we  find  the  following: 

Table  VIII.  A  single  reinforcing  rod,  without  end  an- 
chorage, will  not  suffice,  since  beams  with  a  value  of  C= 
279,700  or  more  have  'too  great  a  minimum  span  length. 
The  same  is  true  if  we  take  C=  139,900  and  use  two  rods. 
At  C=93,200,  using  three  rods,  we  could  use  a  beam  16^2" 
wide  and  16^>"  deep  with  three  I"  square  rods  as  rein- 
forcement (as  the  minimum  span  is  here  16.5  ft.).  This 
would  not  be  a  good  beam  and  would  not  be  economical. 

Table  IX.  Neither  one  nor  two  rod  beams  can  be 
used  here  for  the  same  reason  as  stated  in  the  foregoing 
paragraph.  It  is  also  seen  that  when  C=93,200  the  mini- 
mum span  is  over  18  ft.  The  conclusion  is  that  a  beam 
for  this  case  needs  shear  reinforcement. 

Table  X.  Here  a  beam  10%"  wide  and  20^"  deep  with 
three  %"  square  rods  has  a  value  C=31 1,000,  which  is 
more  than  required.  The  area  of  steel  reinforcement 
could  be  reduced  by  taking  280/311  of  the  total  and  mak- 
ing the  two  straight  rods  of  smaller  section,  but  as  this 
gives  13/16",  an  odd  size,  for  their  diameter  it  is  hardly 
worth  while.  One  of  these  rods,  the  middle  one,  must 
be  curved  up  and  run  beyond  the  edge  of  support  50  dia- 
meters, or  otherwise  anchored  at  the  supports  of  the  beam. 

67 


Table  XI.  Here  we  find  that  a  beam  7"  wide  and  24" 
deep  with  three  %"  round  rods  comes  near  meeting  all  the 
requirements.  One  of  these  rods  must  be  curved  up  and 
anchored. 

Table  XII.  In  this  table  the  beam  7^"  wide  and  22y4" 
deep  with  four  11/16"  square  rods  meets  all  the  require- 
ments. Two  of  these  rods  must  be  curved  up  and  an- 
chored. 

Table  XIII.  In  this  table  the  beam  7"  wide  and  23^" 
deep  with  four  y±"  round  rods  comes  close  to  meeting  all 
requirements.  Two  of  these  rods  must  be  curved  up  and 
anchored. 

The  proper  beam  for  this  case  may  be  determined  by 
the  desired  depth  or  by  the  availability  of  round  or  square 
rods. 

In  the  very  deep  beams  one-eighth  of  'the  depth  of 
beam  may  be  more  than  necessary  below  the  center  of 
the  rods.  The  standard  beam  of  these  tables  has  an 
effective  depth  of  17/24  of  the  outside  depth  of  the  con- 
crete rectangle.  If  the  rods  are  dropped  so  that  this 
effective  depth  (distance  from  centroid  of  compression 
in  the  concrete  to  the  center  of  steel)  is  increased,  the 
coefficient  C  of  the  strength  of  the  beam  is  increased  pro- 
portionally. Thus  at  a  depth  of  48"  the  standard  beam 
would  have  the  rods  l/&  of  the  depth  or  6"  from  the  bot- 
tom. The  effective  depth  is  17/24  of  this  or  34".  If  it  is 
desired  to  place  the  rods  4"  above  the  bottom  of  the  beam, 
the  effective  depth  is  increased  by  2",  and  C  is  36/34  of 
the  tabular  value. 


TABLE  VIII. 

Reinforced  Concrete  Beams  with  Straight 
Rods  Not  Anchored* 

R'f'n't 
One 
Square 
Rod 
Diam. 
in 
In. 

Sec 
Cone 
Be 

b 
in 

In. 

of 
rete  j 
im 

d 
in 
In. 

Min 
Sp'n 
in 
Ft. 

Prod,  of 
Span  in 
Ft.  and 
Unif'm 
L,oad  in 
Pounds. 

R'f'n't 
One 
Square 
Rod 
Diam. 
in 
In. 

|   Sec.  of 
Concrete 
Beam 

Min 
Sp'n 
in 
Ft. 

1    c 

Prod,  of 
Span  in 
Ft.  and 
Unif'm 
Load  in 
Pounds. 

> 

in 

In. 

d 
in 
In. 

% 

1 

154 
in 

6 

434 
4 

6 

4?4 

2480 
1960 
1650 

1 

4 

454 
454 
43,4 
5 
554 
55^ 

2354 
22 

2034 

1934 

1834 

1734 

1654 

2354 
22 

2034 

1934 
1834 
1734 
1654 

153200 
145400 
137200 
130500 
123900 
117200 
106100 

i5* 

03 

1/2 
134 

754 
6 
554 

754 

6 

554 

4660 
3830 
3390 

3/8 

in 
m 

834 
754 

654 

834 

7/2 

654 

8130 
6970 
5990 

15i 

4^ 
4J4 

554 
554 
5?4 
6 
654 

2654 

2434 

23>4 

2254 

2154 
20/2 

1934 

1834 

2654 
2434 
2354 
2254 
2154 
2054 
1934 
1834 

219600 
206100 
195600 
188200 
179900 
171200 
165200 
155600 

Is 

134 
254 

254 

1054 
9 
8 

754 

1054 
9 
8 
754 

12970 
11390 
10120 
9170 

54 

2 

254 

2/2 

2M 

im 

1054 
954 
854 

1134 
1054 
954 
854 

19420 
17350 
15700 
14050 

154 

5 
554 
554 
53,4 
6 
654 
6y2 
634 

2954 

2734 

2654 
2554 
2454 
2354 
22/2 

2154 

2034 

2954 
2734 

2654 
2554 
2454 
2354 
22  V3 
2154 

2034 

302200 
286400 
273600 
259700 
249900 
239300 
232400 
221000 
213500 

ft 

254 
254 

JK 

354 

1354 
1134 
1034 
934 
954 

1354 
1134 
1034 
934 
954 

27700 
24400 
22500 
20200 
19300 

M 

2/2 

234 
3 
354 

354 

14/2 
1354 
1254 
1154 
1054 

14/2 

1354 
1254 
1154 
1054 

37200 
34200 
31600 
29000 
27100 

i$f 

5/ 
534 
6 
654 
654 
63/4 

754 
754 
734 

32 

3034 

2954 
2854 
2754 
2654 
2554 
2454 
2354 
2234 

32 

3034 

2954 
2854 
2754 
2654 
2554 
2454 
2354 
2234 

399000 
384300 
368700 
353000 
340500 
328000 
315500 
302000 
293400 
284100 

U 

23/4 

3 

354 

354 
3?4 

16 

143,4 

13/2 

1254 
1154 

16 

1434 
1354 
1254 

11/2 

49900 
46100 
41900 
38700 
35100 

X 

3 

354 
354 
334 
4 
454 

17/2 

1654 
IS 
14 
1354 
12*4 

17/2 

1654 
15 
14 
1354 
1254 

65100 
60400 
55800 
52100 
49300 
46500 

154 

6 

654 
654 
634 

754 

754 

I* 

854 
854 

35 

3354 

if* 

30 
29 
28 

27 
2654 
2554 
2434 

35 
3354 
3254 
31 
30 
29 
28 
27 
2654 
25/2 
2434 

520600 
496800 
478800 
459500 
446200 
431400 
416500 
400200 
390500 
379300 
368200 

H 

3/2 

334 

454 
454 
434 

20/2 
19 
18 
1634 
16 
IS 
14i4 

20/2 
19 
18 
1654 
16 
15 

H/2 

103700 
95900 
91100 
84500 
81000 
75700 
73400 

TABLE  IX. 

Reinforced  Concrete  Beams  with  Straight 

Rods  Not  Anchored* 

R'f'n't 
One 

Sec.  of 
Concrete 

c 

Prod,  of 

R'f'n't  |    Sec.  of 
One     |  Concrete 

1     c 

|  Prod,  of 

Round 

Beam 

Min 

Span  in 

Round 

Beam 

Min 

Span  in 

"Rnrl 

Sp'n 

Ft    and 

Rod 

Diam. 

h 

d 

in 

Unif'm 

Diam. 

h 

d 

in 

Unif'm 

in 

in 

in 

Ft. 

Load  in 

in 

in 

in 

Ft.  (Load  in 

In. 

In. 

In. 

Pounds. 

In.      |  In. 

In. 

J  Pounds. 

« 

6 

6     I       1910 

354 

225412254!   116500 

54 

1 

454 

4541        1430 

354 

21 

21 

109000 

15* 

4 

4     |        1300 

l 

354 

1954 

1954 

101000 

I56 

I 
15* 

1  I// 

754 
Stf 

754 
524 

3680 
2920 
2540 

454 
454 

io/4 

1754 
1654 

10/4 

1754 
1654 

89600 
84200 

354(2654 
35412454 

2654 
2454 

174100 
162600 

154 

854 

854 

6020 

tt 

iv* 

7 

7 

5110 

4 

?V/f 

23X4 

152800 

m 

654 

654 

4560 

156 

454 

2154 

2154 

142400 

& 

15* 

154 

1M 

1154 
954 
8 

H54 
954 
8 

112CO 
9090 
7930 

454 
454 

Ml/2 

1954 
1854 

2054 
1954 
1854 

133900 
127900 
121200 

2 

7 

7 

6940 

4 

2854 

2854 

233300 

X 

154 

154 

2 
254 

1254 
1054 
954 
8^ 

1254 
1054 
954 
854 

15800 
13600 
12600 
10700 

154 

454 
454 
4« 

554 

27 
2554 
24 
23 

2154 

27 

2554 
24 
23 
2154 

219100 
206900 
193800 
186600 
175900 

154 

1354 

1354 

21800 

554  2054 

2054|    167700 

& 

254 

2/2 

1154 
1054 
954 

1154 
1054 
954 

18700 
16700 
15200 

454 
454 
454 

3254 
3054 
2954 

3254 
3054 
2954 

318000 
301400 
287100 

H 

2 

254 

254 

254 

1454 
1254 
1154 

10  54 

1454 

i2y4 
1154 
1054 

29400 
25900 
23300 
21300 

IH 

5 

554 
554 
554 
6 

2/54 
2654 
2554 
24 
23 

2754 
2654 
2554 
24 
23 

272400 
260100 
247900 
234600 
224800 

H 

25* 

254 

254 

1554 
139* 

1254 
1154 

1554 
13M 
1254 
ll/2 

38000 
33500 
30400 
28100 

454 
5 
554 
5'/? 

3454 
33 
3154 
30 

3454 
33 
3154 
30 

406000 
385500 
368000 
350500 

M 

25* 

254 
254 
3 

1854 
1654 
15 
1354 

1854 
1654 
15 
1354 

531(70 
48200 
43800 
40200 

154 

5* 

654 
654 

2854 
2754 
2654 
2554 

2854 
2754 
2654 
2554 

335900 
321300 
309600 
297700 

354 

12^4 

1J& 

37300 

2ft 

2054 

2054 

81500 

3 

18« 

1854 

74700 

H 

354 

1754 

1754 

68500 

354 

16 

16 

63500 

354 

15 

15 

59600 

Reinforced  Concrete  Beams— One  Rod 
Curved  Up  and  Anchored. 


R'f'n't 
Three 
Square 
Rods 
Diam. 
in 
In. 

Sec 
Cone 

B€£ 

b 
in 
In. 

of 
rete 

un 

d 
in 
In. 

Min| 
Sp'n 
in 
Ft.  | 

C 

Prod,  of 
Span  in 
Ft.  and 
Unif'm 
Load  in 
Pounds. 

R'f'n't 
Three 
Square 
Rods 
Diam. 
in 
In. 

Sec 
Con 
Be 

b 
in 
In. 

of 
:rete 
am 

~ 
in 
In. 

Min 
Sp'n 
in 
Ft. 

C 
Prod,  of 
Span  in 
Ft.  and 
Unif'm 
Load  in 
[Pounds. 

l/4 

2 
254 

854 

5M 

6.2 
5.0 
4.1 

10900 
8680 
7030 

1 

8 
8H 
9 

9y2 

10 

wy2 
11 
1154 

12 

35 
33 
31 
2954 
28 
2654 
25/2 
2454 
2-354 

24.8 
23.4 
22.0 
20.9 
19.8 
19.0 
18.1 
17.2 
16.5 

694000 
654000 
613000 
585000 
555000 
531000 
506000 
479000 
460000 

& 

2J4I11 
3     |   954 
35^1   754 

7.8 
6.6 

5.5 

21300 
17900 
14900 

H 

3 

3J4 

JH 

13 

H54 
10 

854 

9.2 
8.0 
7.1 
.6.2 

35900 
31400 
27900 
24400 

I'tf 

9 

9^ 
10 
10J4 
11 
11J4 
12 
12J4 
13 

3954 
3754 
35  y, 
3354 
3254 
3054 
2954 
2854 
2754 

27.8 
26.4 
25.1 
23.9 
22.8 
21.8 
20.9 
20.0 
19.3 

982000 
934000 
891000 
847000 
810000 
770000 
740000 
707000 
684000 

& 

3/2 

454 

1554 
13J4 
12 

1054 

10.81     57700 
9.6|      51300 
8.5|     45600 
7.6]     40800 

54 

4 

454 

$l/2 

6 

17J/2 
1554 
14 
1254 
1154 

12.4 
11.0 
9.9 
9.0 
8.3 

86800 
76600 
69400 
63200 
58300 

l« 

10 
1054 
11 
1154 
12 

i2y2 

13 

1354 
14 

1454 

4354 
4154 
3954 
38 
3654 
35 
3354 
325^ 
3154 
3054 

31.0 
29.6 
28.2 
26.9 
25.9 
24.8 
23.9 
23.0 
22.1 
21.4 

1356000 
129400-0 
1231000 
1176000 
1131000 
1085000 
1046000 
1007000 
969000 
937000 

* 

4/2 

5 

554 

6 

654 

1954 
1754 
16 
1454 
1354 

14.0 
12.6 
11.3 
10.5 
9.6 

123900 
111400 
99700 
92500 
83900 

N 

5 
554 
6 

6y2 

7l/2 

22 
20 

1854 

1654 
1554 
1454 

15.6 
14.2 
12.9 
11.9 
11.2 
10.3 

170400 
154900 
141600 
129200 
122000 
111700 

i£ 

11 
11J4 
12 
1254 
13 
1354 
14 
1454 
15 
1554 
16 

48 
46 
44 
4254 
4054 
3954 
3754 
3654 
3554 
3454 
33 

34.0 
32.6 
31.2 
29.9 
28.9 
27.8 
26.7 
25.9 
25.0 
24.3 
23.4 

1795000 
1724000 
1646000 
1581000 
1528000 
1472000 
1413000 
1368000 
1320000 
1284000 
1234000 

U 

i>54 
s 

6y2 

754 

8 

24 
22 
2054 
19 
1754 
1654 

17.0 
15.6 
14.3 
13.5 
12.6 
11.7 

224400 
205700 
188800 
178100 
166400 
154300 

K 

6 

<* 

754 
8 
854 
9 

2654 
24  y4 
22y2 
21 
1954 
1854 
1754 

18.6 
17.2 
15.9 
14.9 
14.0 
13.1 
12.4 

292900 
270500 
251000 
234300 
220300 
206100 
195200 

IH 

12 
1254 
13 
1354 
14 
1454 
15 
1554 
16 
1654  ' 
17     i 
1754 

5254 
5054 
4854 
4654 
45 
435^ 
42 
4054 
3954 
3854 
37 
36 

37.2  2343000 
35.8  2254000 
34.3|2164000 
33.1  [2086000 
31.9(2008000 
30.8(1941000 
29.7(1874000 
28.7)1801000 
28.0(1762000 
27.1(1707000 
26.2(1648000 
25.511606000 

H 

7     |30^4  21.  8|   467000 
754|2854|20.  2|  432000 
8     |2654|19.0|  406000 
854|2554|17.9|   383000 
9     |2354|16.  8|   360000 
95412254(15.  9(   341000 
10     I21J4I15.2I   327000 
1054!2054|14.5(   311000 

TABLE   XI. 

Reinforced  Concrete  Beams  --One  Rod 
Curved  Up  and  Anchored. 

R'f'n't 
Three 
Round 
Rods 
Diam. 
in 
In. 

Sec.   of 
Concrete 
Beam 

Min 
Sp'n 
in 
Ft. 

C 

Prod,  of 
Span  in 
Ft.  and 
Unif'm 
Load  in 
Pounds. 

R'f'n't 
Three 
Round 
Rods 
Diam. 
in 
In. 

Sec.  of 
1  Concrete 
1     Beam 
1 

Min 
Sp'n 
in 
Ft. 

C 

Prod,  of 
Span  in 
Ft.  and 
Unif'm 
Load  in 
|  Pounds. 

b 
in 
In. 

d 

in 
In. 

b 
in 
In. 

d 
in 
In. 

tt 

154 
zy* 

954 
554 

6.6 
5.0 
3.9 

9010 
6820 
5360 

1 

ft 

5* 

sy2 

9 

9l/2 

3334 
3154 
2954 
27^ 
26 
24^ 
23^ 

[23.9 
22.3 
20.7 
19.5 
18.4 
17.4 
16.5 

1    524000 
491000 
|   455000 
428000 
405000 
|    382000 
362000 

ft 

¥ 

1034 
854 
754 

|   7.6 
6.0 
5.1 

16400 
12800 
11000 

N 

f% 

354 

12/4 

1054 

8*4 

8.7 
7.3 
6.2 

26600 
22300 
19000 

13* 

7 

7y2 

8 

sy2 

9 

9K 
10 

IOH 

3934 
37 

34?4 

!?« 

2954 

2734 

26^ 

28.2 
26.2 
24.6 
23.2 
22.0 
20.7 
19.7 
18.8 

783000 
727000 
684000 
646000 
611000 
576000 
545000 
522000 

ft 

3 

w 

14 
12 

1054 

9.9 

8.5 
7.4 

41700 
35700 
31200 

l/2 

35^1534 

4      |1334 

454|i254 

11.2 
9.7 
8.7 

61300 
53500 
47700 

I* 

8 

sy2 

9 

9/2 

10 

ioy2 
11 
11% 

43 

40K 
3854 
3654 
34K 
3234 

3154 
30 

30.5 
28.7 
27.1 
25.7 
24.4 
23.2 
22.1 
21.2 

1047000 
986000 
931000 
882000 
840000 
797000 
761000 
730000 

354 

ft         4 

ir< 

20 

1754 
1554 
14 

14.2 
12.4 
11.0 
9.9 

98600 
86300 
76400 
69000 

H 

•r* 

SIA 

2154 
19 
1754 
1554 

15.2 
13.5 
12.2 
11.0 

131000 
115000 
105000 
93600 

1H 

9 
9X 

10 
IQtf 

11 

ny2 

12 

I2J4 

13 

46J4 
4334 
4154 
3954 
3734 

36>4 
3434 

33/4 
32 

32.8 
31.0 
29.4 
28.0 
26.7 
25.7 
24.6 
23.5 
22.7, 

1362000 
1288000 
1220000 
1160000 
1110000 
1068000 
1023000 
979000 
942000 

ii 

454 

554 
6 

654. 

23 

2034 

19 

1754 
16 

16.3 
14.7 
13.5 
12.2 
11.  3j 

168600 
152500 
139900 
126400 
117800 

M 

ly, 

6 

r* 

2434 
2254 

2054 

19 

17*4 

17.5|  216900 
15.9     197200 
14.5)    178600 
13.51    166200 
12.6J   155500 

iK 

10     | 

toj* 

11 

ny2 

12 
12J4 

13 

13^ 

14      | 

4954 
47 
45 
43 
4154 
3954 
38 
3634 
3554 

35.1| 
33.3 
31.9 
30.5 
29.2 
28.0 
26.9 
26.0 
25.0 

1735000 
1643000 
1577000 
1506000 
1446000 
1381000 
1330000 
1288000 
1232000 

554 
6 

H               654| 

7y2 
8 

3054 
28 

2/<  ' 

22H 
21 

21.6|    362000 
19.  8|    333000 
18.4|   310000 
17.  0|   285600 
15.9|   268300 
14.  9     249900 

TABLE   XII. 


Reinforced  Concrete  Beams— Two  Rods 
Curved  Up  and  Anchored. 


R'f'n't 
Four 
Square 
Rods 
Diam. 
in 
In. 

Sec.  of 
Concrete 
Beam 

C 
]Prod.  of 
Min  j  Span  in 
Sp'n|Ft.  and 
in      Unif'm 
Ft.  |  Load  in 
|  Pounds. 

R'f'n't 
Four 
Square 
Rods 
Diam. 
in 
In. 

Sec.  of 
Concrete 
Beam 

Min 
Sp'n 
in 
Ft. 

C 
Prod,  of 
Span  in 
Ft.  and 
Unif'm 
Load  in 
Pounds. 

b 
in 
In. 

d 

in 
In. 

b 
in 
In. 

d 
in 
In. 

/4 

!* 

9^4 
7?4 

4.9 
4.1 

15200 
12800 

1 

10 
10H 
11 

ny2 

12 

37J4 
35^ 
34 
32^ 
31 

19.8 
18.9 
18.1 
17.3 
16.5 

983000 
937000 
899000 
860000 
817000 

* 

3K'H^ 
3541  9*4 

6.0|     29100 
5.2|     25200 

tf 

4 

4H 

13  J4 

1134 

7.01     49300 
6.3J     43700 

IX 

iiH 

12 

12H 
13 

13/2 

41 

39^ 
373,4 

36^4 
35 

21.8 
21.0 
20.1 
19.3 
18.6 

1369000 
1322000 
1262000 
1210000 
1171000 

& 

434115 
5J4J13J4 

8.0|     75700 
7.2J     67800 

K 

5H 
6 

18K 

15# 

10.0|    124000 
9.0J    112400 
8.2|    102100 

l« 

12^ 
13 
13^ 
14 
14J4 
15 

l4lM 

43^4 
4134 

40^ 
39 

24.9 
23.9 
23.0 
22.2 
21.4 
20.7 

1932000 
1859000 
1787000 
1725000 
1663000 
1611000 

ft 

534|20^|10.  9|    171200 
6^4119      |10.1|    159000 
634|17H|   9.3J    146400 

M 

6H 

7/2 

22J4 
20  M 
19^ 

12.0 
11.0 
10.4 

233000 
213500 
202000 

IH 

14 
14^ 
15 

isy2 

16 

16H 

50^ 

%* 

45  H 
44 
4234 

26.9 
25.9 
25.0 
24.2 
23.4 
22.7 

2525000 
2438000 
2347000 
2273000 
2194000 
2136000 

|i 

7MI24^|12.9|   302000 
7#  22#  12.1    284000 
8J4|21#|11.4|  269000 

1^ 

15 
IStf 

16 

16^ 
17 
17^ 
18 

56 
54^4 
52H 
51 
49H 
48 
46?4 

29.8 
28.8 
27.9 
27.1 
26.3 
25.5 
24.9 

3332000 
3228000 
3124000 
3035000 
2945000 
2856000 
2782000 

¥4 

7K 

8 
8fc 

9 

28     |14.9 
26^|14.0 
24^|13.  2 
23^|12.4 

417000 
391000 
368000 
345000 

9 

9y2 

H    |io 
\ioy2 

31^4 
30 
28^ 

27M 

16.9 
16.0 
15.2 
14.5 

643000 
606000 
575000 
552000 

^ 

TABLE   XIII. 

Reinforced  Concrete  Beams—  Two  Rods 
Curved  Up  and  Anchored, 

R'f'n't 
Four 
Round 
Rods 
Diam. 
in 
In. 

Sec.  of 
Concrete 
Beam 

b         d 
in       in 
In.      In. 

Min 

ISp'n 
in 
Ft. 

C 
Prod.-  of 
Span  in 
|Ft.  and 
Unif'm 
Load  in 
j  Pounds. 

R'f'n't      Sec.  of 
Four    |  Concrete 
Round       Beam 

RnH<- 

|  Prod,  of 
Min  )  Span  in 
Sp'nJFt.  and 
in   |  Unif'm 
Ft.  |Load  in 
J          j  Pounds. 

Diam.       b 
in          in 
In.         In. 

d 
in 

In. 

/4 

2      1   9y4\   4.9 
2l/2\  754J   3.9 

12000 
9400 

8 

i        854 

9 

954 

3634 
32  J/2 

19.5     763000 
18.3     717000 
17.3     673000 
16.3     636000 

2y2  ny2 

3        9/2 

6.  If     23300 
5.1|     19200 

\  9 
l/s        954 
10 

|1054 

39 
37 

21.9)1084000 
20.7)1024000 
19.7)   970000 
18.7)   924000 

H 

3       1334 
3J4  UK 

7.3 
6.3 

40200 
34200 

& 

3^)16 
4     |14 

8.5f     63500 
7.5|     55500 

|10 

154      H  2 
11J4 

4534 
4334 
4134 
40 
3854 

24.311483000 
23.3)1420000 
22.2)1355000 
21.3  1298000 
20.3)1241000 

y* 

4       18541   9.7)     94400 
454  1654]  8.6J     84200 

ft         454I205^|10.9[   134000 
|   5     |1854|   9.8|   121200 

11 

13/6        12 

1  125-^ 

soy2 

4654 
44J4 
4234 

26.9|1983000 
25.7)1896000 
24.6)1816000 
23.5)1734000 
22.7)1679000 

5      23 
6  2  19  4 

12.2 
11.0 
10.1 

186600 
167700 
153400 

ii 

6  2|23  4|12'.2 
6y2  21J4I11.3 

248000 
225000 
208000 

12 

154       13 

14  2 

55 
5234 

5034 

49 

47 

29.2)2570000 
28.0)2464000 
27.0  2372000 
26.1)2290000 
25.0)2191000 

,4 

6       27y2 

T2  2354 

14.6 
13.6 
12.5 

321000 
298000 
274000 

H 

7      32 
7l/2  30 
8       28 

17.0 
16.0 
14.9 

508000 
477000 
444000 

CHAPTER  VII. 
Girders. 

In  building  work  a  girder  is  usually  understood  to  be  a 
large-sized  beam,  whether  rolled  or  built,  particularly  a 
beam  that  carries  smaller  floor  beams. 

The  selection  of  the  size  of  a  rolled  beam  acting  as  a 
girder  may,  of  course,  be  done  in  the  same  manner  as  in 
'the  case  of  simple  beams,  if  the  load  is  uniformly  distrib- 
uted along  the  beam.  When  the  load  is  distributed  in 
equal  concentrations  at  equal  intervals,  the  same  method 
may  be  used  with  but  small  error ;  that  is,  the  total  load 
carried  by  the  floor  area  tributary  to  the  girder  may  be 
used  as  a  uniformly  distributed  load.  This  will  need  cor- 
rection only  where  there  is  an  odd  number  of  panels  in 
the  girder,  as  shown  in  the  next  paragraph. 


F'.^.l.  Fig- 2. 

It  will  be  found  that  the  effect  on  the  girder  EF,  Fig.  1, 
of  the  three  beam  concentrations  is  the  same  as  the  total 
floor  load  enclosed  by  the  rectangle  ABCD,  assumed  to 
be  uniformly  distributed  on  the  girder.  The  effect  of  the 
two  beam  concentrations  on  girder  KL,  Fig.  2,  is  less  than 
the  load  GHIJ,  assumed  uniformly  distributed,  by  'the 
fraction  1/72.  The  following  rules  may  then  be  used  in 
designing  girders  in  such  cases. 

75 


Rule  1.  When  there  is  an  even  number  of  equal  panels 
(or  an  odd  number  of  concentrations),  assume  the  load 
tributary  to  a  girder  (the  rectangle  ABCD  of  Fig.  1,  the 
lines  AB  and  CD  being  midway  between  girders,  etc.),  as 
uniformly  distributed  on  the  girder. 

Rule  2.  When  there  is  an  odd  number  of  equal  panels 
(or  an  even  number  of  concentrations),  assume  the  load 
tributary  to  a  girder  as  uniformly  distributed  on  the  gir- 
der, but  deduct  1/72  for  3  panels,  1/200  for  5  panels,  1/392 
for  7  panels,  etc.  The  denominator  of  the  fraction  is 
eight  times  the  square  of  the  number  of  panels.  It  is 
seen  'that  the  deduction  is  scarcely  worth  considering  for 
more  than  three  panels. 

In  all  cases  where  these  rules  apply  a  beam  occurs  at 
each  column  or  each  end  of  the  girder. 

When  the  girders  are  not  parallel,  the  method  of  as- 
suming the  load  to  be  uniformly  distributed  may  still  be 
applied  with  but  little  error,  if  the  lines  AB,  DC,  etc., 
be  drawn  midway  between  girders. 

The  general  method  of  finding  the  bending  moment  on 
a  girder  for  any  system  of  concentrated  loads  is  as  fol- 
lows: 


p. 

dz 

^ 

Rz 

Pt 

l     .                      d5                  , 

L              d-* 

rrr, 

[5  , 

^ 

[ 

r\  i 

t     ) 

X     ( 

f 

x                f 

PloM  -»•  Pzd2-»-F3ol3+  etc 


R\ 


M   -     R\  K  -P\  y  - 
76 


(0 

-(2) 
(3) 


M  is  the  bending  moment  in  foot  pounds,  assuming  that 
all  loads  are  in  pounds  and  all  distances  are  in  feet. 

The  above  is  on  the  assumption  that  the  maximum  mo- 
ment occurs  under  the  load  Pg.  The  maximum  moment 
will  generally  occur  under  a  load  near  the  middle  of 
span.  In  order  to  find  definitely  which  load  is  the  critical 
one,  first  find  the  reaction  Ri,  as  indicated,  then  subtract 
successively  Pi,  P2,  P3,  etc.,  until  the  load  is  found  where 
the  "shear  passes  through  zero,"  that  is,  where  a  nega- 
tive value  is  obtained  in  this  subtracting  process. 

As  a  rough  check  this  moment  should  be  nearly  equal 
to  half  the  sum  of  the  products  of  each  several  load  and 
the  distance  to  the  nearest  support.  (See  Godfrey's  Ta- 
bles, page  43.) 

To  use  this  bending  moment  in  the  beam  and  girder 
tables  multiply  it  by  eight  and  use  that  product  as  C  in  the 
tables,  or  divide  it  by  250  and  use  that  quotient  as  Q  in  the 
tables  of  rolled  beams. 

Sometimes  an  I-beam  is  reinforced  by  the  addition  of  top 
and  bottom  flange  plates.  This  is  not  economic  construc- 
tion, but  is  occasionally  necessary  to  keep  down  the  depth. 
It  is  also  done  sometimes  to  reinforce  existing  beams  in 
place.  The  punching  or  drilling  of  holes  in  the  flange  of 
a  beam  diminishes  the  strength  of  that  beam  in  the  ten- 
sion flange,  and  this  must  be  considered  in  calculating  the 
reinforcement  added  by  the  flange  plate.  In  order  to 
minimize  this  deduction  of  area  rivet  holes  should  not  be 
located  opposite  one  another  in  the  flanges,  but  should  be 
alternated,  except  near  the  ends  of  the  plate.  Here,  how- 
ever, the  bending  moment  is  less  than  at  the  middle  of 
span. 

Table  I  gives  coefficients  for  finding  the  load  bearing  ca- 
pacity of  standard  I-beams  with  flange  plates,  as  well  as 
the  length  of  plate  required  in  terms  of  the  length  of  span. 
These  tables  are  figured  with  'two  holes  out  of  beam  and 
plate  in  both  top  and  bottom  flanges. 

Box  girders  made  of  two  channels  and  cover  plates  or 
two  I-beams  and  cover  plates  are  frequently  used  under 

77 


TABLE    I. 

Capacity  of  I  Beams  with  Flange 

Plates. 

Size  of 

|   Size  of  Top 
|     and  Bottom 

Length  of            Q 
Fl'nge  Plate  I  Prod.       of 

I-Beam 

Flange  Plate 
Iin  Inches. 

Portion  of 
Span. 

Safe  Ld.  in 
T'ns  &  Sp'n 

in  Feet. 

10"     25 

Ib. 

7xJi 

.79 

187.  1 

10"     25 

Ib. 

7XH 

.87 

254.2 

12"     31.5 

Ib. 

7xt/s 

.74 

258.3 

12"     31.5 

Ib. 

7x5/1 

.83 

337.9 

15"     42 

Ib. 

8x*/2 

.77 

469.4 

15"     42 

Ib. 

8x^4 

.84 

588.6 

18"     55 

Ib. 

9x*/2 

.75 

693.7 

18"     55 

Ib. 

9xJ4 

.82 

859.8 

20"     65 

Ib. 

9xy2 

.70 

857.6 

20"     65 

Ib. 

9x$4 

.79 

1041.0 

24"     80 

Ib. 

10X^2 

.70 

1244.0 

24"     80 

Ib.                   10x^4 

.77          1         1495.0 

TABLE    II. 

Capacity  of  Channel  Beams  with 
Cover  Plates. 

2  Channels 
Size. 

Size  of  Top 
and  Bottom 
Cover  Plate 
in  Inches. 

Length  of 
Bot.  Plate 
Portion  of 
Span. 

Q 
Prod,    of 
Safe     Ld.     in 
Tons     &  Span 
in    Feet. 

7"        9.75   Ib. 
7"       9.75  Ib. 
8"     11.25  Ib. 
8"     11.25  Ib. 
9"     13.25  Ib. 
9"     13.25  Ib. 
10"     15         Ib. 
10"      15         Ib. 
12"     20.5     Ib. 
12"     20.5     Ib. 
15"     33         Ib. 
15"     33         Ib. 

9*l/4 
9xy2 
9xy4 

9xy2 

9xJ4 
9x^ 
12xf6 
12x^ 
12x^ 
12x*4 
18xJ^ 
18x34 

.83 
.93 
.80 
.90 
.78 
.89 
.87 
.93 
.86 
.91 
.86 
.91 

112.6 
180.6 
134.5 
209.3 
161.8 
245.7 
303.4 
436.9 
491.4 
651.0 
993.0 
1310.0 

78 


walls  and  sometimes  in  other  locations.  Table  II  gives 
a  number  of  such  box  girders  and  coefficients  for  finding 
the  load  bearing  capacity.  Generally  the  top  plate  is 
run  the  full  length.  The  bottom  plate  may  be  made  short- 
er, as  indicated  in  the  table. 

The  values  in  the  third  column  of  Tables  I  and  II  are 
.06  greater  than  the  theoretical  length  of  cover  plate  re- 
quired. This  is  to  allow  for  rivets  near  the  ends  of  the 
plates.  The  rivets  should  be  spcaed  3  inches  apart  for  a 
short  ditsance  at  the  ends  of  the  plates. 

Examples. 

(1)  Given  a  12-inch  31  J^-lb.  I-beam  in  place  that  is  to 
be  reinforced  so  that  on  a  span  of  16  ft.  it  will  carry  20 
tons.     The  value   of   Q  should  be  20X16=320.     By  ref- 
erence to  Table  I  it  is  seen  that  this  comes  between  the 
two  values  of  Q  for  a  12-inch  I-beam.     By  interpolation 
it  is  found  that  7"X9/16"  flange  plates  will  be  required. 
Interpolating   again   these   plates    should   be   about   .81    of 
the  span  in  length,  or  13  feet. 

(2)  Given  a  9-in.  wall  six  feet  high  carrying  a  roof  slab, 
whose  total  load  is  900  Ibs.  per  foot.     The  span  is  15  feet. 
The  weight  of  the  wall  is  90X6X15=8,100,  and  the  roof 
load  is  900X15=13,500,  a  total  of  10.8  tons.     Q  is  10.8X 
15=162.     By  reference  to  Table  II  it  is  seen  that  2  9-in. 
13.25-lb.  channels  with  9"X^4"  top  and  bottom  cover  plates 
will   meet  the   requirements.     The  top  plate   may  be   full 
length  and  the  bottom  plate  .78X15,  or  say  12  feet  long. 

(3)  Given  a  bay  window,  the  walls  of  which  are  sup- 
ported  on   columns   at   the   first   floor.     Find   the    size   of 
box  girder  of  channels  and  plates  for  the  following  data: 
Span,  12  ft. ;  weight  of  wall,  72,000  Ibs. ;  weight  of  floors, 
48,000  Ibs.     The   total   load  carried   is    120,000  Ibs.,   or  60 
tons.     Q  is  60X12=720.    In  Table  II  it  is  seen  that  2  15- 
in.   channels    and   two    18"X/4"   plates   would   have   more 
strength  than  necessary.     It  is  also  seen  that  W  in  thick- 
ness of  the  cover  plates  adds  or  deducts  about  150  in  the 
value  of  Q.     Hence  with  18"X&$"  plates  Q  is  about  840. 
This  size  of  plates  could  then  be  used.    Both  plates  should 

79 


be  full  length ;  the  lower  plate  can  act  as  a  bearing  plate 
on  the  column. 

PLATE    GIRDERS. 

In  a  plate  girder  there  are  several  points  of  design  that 
must  be  considered. 

First — The  section  of  the  flanges  must  be  sufficient  to 
take  the  longitudinal  stresses  resulting  from  the  maximum 
bending  moment. 

Second — The  web  plate  must  be  thick  enough  to  take 
the  maximum  shear. 

Third — The  rivets  in  the  flange  angles  connecting  the 
same  to  the  web  must  be  sufficient  to  take  the  flange  stress 
from  web  to  flange. 

Fourth — The  web  plate  must  be  stiffened  against  buck- 
ling, if  it  is  not  of  sufficient  rigidity  in  itself  to  take  the 
shear  without  buckling. 

Fifth — There  must  be  end  stiffeners  designed  to  take  the 
full  reaction  of  the  girder  and  to  transmit  the  same  into 
the  web  plate. 

Tables  III  and  IV  give  170  girders  and  coefficients  to 
determine  the  capacity  of  the  same.  The  number  may 
be  indefinitely  extended  by  interpolating  for  different 
thicknesses  of  flange  plates  or  angles.  Also  by  noting  the 
increase  in  the  value  of  Qi  and  Q2  per  inch  increase  in 
depth  of  web,  in  the  various  pairs  of  groups  of  girders 
having  the  same  flanges,  the  value  of  these  coefficients  for 
different  depths  may  readily  be  found.  (These  tables  are 
based  on  tables  in  "Godfrey's  Tables,"  pages  94  to  98  in- 
clusive.) The  depth  of  girder  back  to  back  of  angles  is 
;4  in.  more  than  the  depth  of  web  plate.  The  coefficient 
Q2  is  to  be  used  only  when  the  web  plate  of  the  entire 
girder  is  in  one  piece  or  is  spliced  for  bending  with  extra 
flange  plates  or  extra  side  plates  near  the  top  and  bottom  of 
the  girder  to  take  the  flange  stress  assumed  to  be  carried 
by  one-eighth  of  the  web  of  the  girder.  The  unit  stress 
of  15,000  Ibs.  per  sq.  in.  is  used  here  because  it  is  be- 
lieved that  a  member  made  up  of  several  pieces  acting 
together  does  not  have  the  same  uniformity  of  distribu- 

80 


TABLE   III. 


Capacity  of  Plate  Girders* 


Unit  stress  15,000  Ibs.  per  sq.  in. 

inches. 


All  Dimensions 


in 


Angles 


C'v'r  | 
Plate 


Part 

of  W'b 

(Inc.  in 
Flngs. 


I      Q, 

I  1A  of 
feb 

Inc.  in 
Flngs. 


Angles 


C'v'r 
Plate 


W'b 


Qi    1    0. 

No 

Part      H  of 
of  W'b  |  Web 
Inc.  injlnc.  in 
Flngs.    Flngs. 


163. 
301. 
262. 
363. 
501. 


213.0 
351.0 
312.0 
413.4 
551.4 


3^x3     x-fr 
354x3     xft 


6  WT2 

2  448.2 

2|  397.2 

6]  520.2 

2|  691.8 


8xA 


308 
575 
510 
718 
986 


386 
652 
593 
796 
1063 


2y3x2y3xy3 


201. 
373. 
322. 
444. 
616. 


407 
763 
668 
934 
1291 


539 
894 
800 
1066 
1423 


7xy2\  ™ 


184. 
345. 
306 
431 
592 


234.6 
394.8 
356.4 
481.8 
642.6 


4  x3  xAI 

4  x3  x 

4  x3>  x 

4  x3  x 

4  x3  x 


4  x3  xA 

4  x3  x^ 

4  x3  xTsg 

4  x3  xA 

4  x3  x5^ 


340 
636 
574 
814 
1111 


418 
713 
651 
892 
1189 


228. 
427. 
376. 
527, 
^26_ 
207, 
389. 
352, 
501, 
683 


303.6 
502.8 
451.8 
603.0 


9xA 


6|   802.8 
258.0" 


~449 
842 
750| 
10591 
14531 


581 
974 
882 
1192 
1585 


439.2 
402.6 
552.0 
733.2 


5  x3 
5  x3 
5  x3 


527] 
984| 
921| 
1327] 
1785] 


622 
1078 
1016 
1422 
1879 


354x254x54 


354x254x54 


8x54 
8x54 


256 
481. 
432 
612 
837. 


^78" 
514, 
448 
622 
860 


8]  332.4 

8|  556.8 

61  508.2 

6]  688.2 

6]  913.2 


5  x3 

5  x3 

5  x3 

5  x3 

5  x3 


4]  355.8 

8 |  592.2 

2]  526.2 

8  700.8 

4]  937.8 


11x54 

11x3/4 


"679] 
1271| 
1177| 
1687 
2280] 


831 
1423 
1329 
1840 
2432 


3  x3  xT5g 

3  x3  x^ 

3  x3  xT5g 

3  x3  xA 

3  x3  xM 


-B 


7x 


3  x3     xA 

3  x3     x^ 

3  x3 

3  x3 

3  x3 


xAI 


7xA 


8x34 
8x34 


|  369. 
|  684. 
|  588. 
811. 
1127. 


01   500.4 

0  S15.4 

01  720.0 
8|    944.4 
411260.0 


8x3^ 
8x34 


435 
805 
701 
977 

1349) 


529 
898 
796 
1070 
1443 


564| 

«S       10471 
x|        901| 
%  I      1246] 
I      17321 


716 
1198 
1053 
1398 
1883 


TABLE    IV. 

Capacity  of  Plate  Girders* 

Unit  stress  15,000  Ibs.  per  sq.  in.     All  dimensions 
in  inches. 


0             Q, 

I      Q             Q, 

No    I 

No 

Angles 

C'v'r 
Plate 

Part  |  y&  of 
W'b|ofW'b|   Web 

Angles 

C'v'r 
Plate  | 

W'b 

Part 
of  W'bl 

VA 

[nc.  in]  Inc.  in 

[nc.  in 

Inc.  in 

Flngs.  |  Flngs. 

Flngs. 

Flngs. 

5     x3  y2x3/f, 

613]        725 

x6     xy2 

1753 

2122 

5     x3y2x$/i 

1147]      1259 

x6     x7^ 

2925 

3294 

5     x3J^x3/6  |llx3/£ 

* 

1042 

1154 

x6     xl/2 

14x14 

^? 

2972 

3344 

5     x3y2x}4  11x3/4 

1483 

1595 

x6     xl/2  114x1 

X 

4223 

4595 

5     x3^2x34 

11X34 

TJ- 

CM 

2018 

2130 

x6     x7/J5|14xl 

T 

5393]      5765 

5     x3J/2x3/6 

776I        951 

6     x6     xl/2\ 

2227]      2807 

1456 

1631 

6     x6     x7^| 

3724|     4303 

.            -y      vj 

1  1  x3/ 

«J9 

1309 

1484 

6     x6     xy2\l4xl/2 

V« 

3747]      4330 

5    x3y2xy«, 

11x34 

X 

1854 

2029 

6     x6     x^|14xl 

0 

5298|      5881 

5     x3^x34 

g 

2535 

2711 

6     x6     x%|14xl       ««           6792]      7374 

r  Ti7  —  JJT" 

790 

921 

6     x6     xy2 

2702 

3539 

6     x3>y2x7/% 

^ 

to 

1463 
1444 

1595 
1576 

6     x6     x7/8 
6     x6     xl/2 

Uxj* 

^ 

4523 
4522 

5359 
5362 

,         XT  £/      $ 

1  •?     7/ 

X 

2121 

2253 

6     x6     xl/2 

14x1 

6372 

7212 

6     x3y2x7^ 

13x7/6 

CM 

2792|      2924 

6     x6     x7^|14xl 

§ 

8190 

9030 

6           31/      JK 

982]      1180 

6     x6     xy2 

3178]      4318 

6       31/xP* 

1825 

2023 

6     x6     x% 

5322 

6462 

6      si/x7 

13x  7 

•e 

1784 

1983 

6     x6     xl/2 

14x}/2 

^ 

5297 

6438 

6     x3y2x% 

13x11 

X 
cq 

2608],     2808 
3449J      3648 

6     x6     xy2 
6     x6     xj^ 

14x1 
14x1 

O 

7445 
9588 

8592 
10730 

A  -    A        i/ 

556 

668 

6     x6     xy2 

3652]      5145 

1039 

1150 

6     x6     x7/$ 

6120|      7614 

4     x4     x3/£ 
4     x4     x^i 
4     x4  c  x?4 

9x1/6 
9x34 
9x34 

* 
X 
rj- 
C-J 

893 
1240 
1724 

1005 
1352 
1836 

6     x6     xl/2 
6     x6     xl/2 
6     x6     xi/% 

14x1 
14x1 

1 

6072       7566 
8520]    10020 
10990]    12490 

707 

882 

6     x6     xy2 

4127 

6330 

I         4      XJ/ 

1326 

1500 

6     x6     x7/& 

6918 

9120 

4     x4     x3/jj 
4     x4     xH 
4     x4     x?4 

9x34 
9x34 

« 

g 

1126]      1301 
15551      1729 
2174]      2348 

6     x6     xl/2 
6     x6     xy2 

6     x6     x7/% 

15x   */ 
15x1^ 
15x1^ 

\  ^ 

2]^ 

7074]     9282 
13070]    15280 
15850]    18070 

6     x4     xJ3 

831 

962 

6     x6     xV2 

46021      7326 

6     x4     xJ/6 

1551 

1682 

6     x6     x7^ 

^o 

77161    10440 

6     x4     XT^ 

ISxi7 

«»H 

1485 

1617 

6     x6     xl/2 

i5x  y 

t        X 

7872]    10600 

6     x4     x-fo 

I3x7/ 

x 

2162 

2294 

6     x6     xl/2 

ISxlJ/ 

;      §       14510|    17250 

6     x4     x?^ 

13x7/6 

C^ 

2880 

3012 

6     x6     x7^|15xl^|    -       17630]   20360 

6     x4     x-fa 

1036 

1234 

8     x8     xy2 

6474|      9582 

6     x4     x7^ 

1939 

2136 

8     x8     xj^ 

Sfi 

10970]    14090 

6     x4     x^r 

13xvk 

-s 

1838 

2037 

8     x8     xl/2 

i8x  y 

z      x      10500]    13610 

13x5/ 

2662 

2862 

8     x8     xy2 

ISxlV 

;   s 

18680]   21800 

6     x4     xj/fj 

13x7/6 

fo 

3563 

3762 

8     x8     x7^|18xlj^|    -1 

23180|   26300 

6     x6     x^ 

12771      1486 

8     x8     xl/2 

7824 

12310 

6     x6     jc7/6 

2126 

2334 

8     x8     xj^ 

X? 

13270 

17750 

6     x6     xj4 

14xi/ 

5H 

2197 

2407 

8     x8     y.l/2 

i8x  y 

;       x      1265C 

17140 

X 

3148 

3359 

8     x8     x^|18xiy 

i      S      22430]   26920 

6     x6     x  7^  |14xl 

5 

3994]      4204 

|8     x8     x7^ll8xl'/|     ^      27870  1    32370 

tion   of  stress   that  single  pieces   such  as   I-beams  would 
show. 

By  selecting  the  girder  according  to  Tables  III  and  IV, 
the  first  requisite  may  be  fulfilled.  When  the  load  is  not 
a  uniformly  distributed  load  or  its  equivalent,  the  maxi- 
mum bending  moment  must  be  found  in  ft.-lbs.,  and  by 
dividing  this  by  250  Tables  III  and  IV  may  be  used, 
since  1/250  of  the  bending  moment  is  equal  to  the  value 
Q  of  these  tables. 

The  shear  in  the  web  plate  should  not  exceed  about 
7,500  Ibs.  per  sq.  in.  of  the  gross  section  of  the  web. 
Hence  to  determine  whether  the  second  requisite  is  ful- 
filled it  must  be  seen  whether  or  not  the  area  of  the  web 
agrees  with  this  condition.  The  maximum  shear  on  a 
girder  in  a  simple  span  is  the  end  reaction.  In  the  case  of 
a  uniformly  loaded  beam  this  is  one-half  of  the  total 
load  carried.  In  other  cases,  as  for  concentrated  loads, 
use  the  methods  of  equations  (1)  and  (2)  to  find  the  re> 
actions.  The  greater  of  these  is  the  maximum  shear.  The 
gross  area  of  the  web  is  the  full  section  of  the  plate,  no 
deduction  being  made  for  rivets.  Thus  a  62"  X  5/16"  web 
plate  will  take  a  shear  of  62X5/16X7,500=145,300  pounds. 

The  spacing  of  rivets  in  the  flange  angles  is  a  detail 
usually  left  to  the  bridge  shop,  where  the  girder  is  made 
or  to  the  draftsman;  but  it  is  also  very  often  carried  out 
in  an  improper  manner.  Sometimes  the  design  is  such  as 
not  to  allow  rivets  enough  in  the  leg  of  angle  connecting 
•to  the  web.  Two  rows  of  rivets  may  be  needed  where 
it  is  only  possible  to  use  one,  as  when  6"X3^2"  angles 
are  used  with  the  31/&-in.  leg  against  the  web.  The  de- 
signer must  bear  this  in  mind  in  selecting  the  section 
of  girder.  If  the  shear  is  such  as  to  require  two  rows  of 
rivets,  a  six-inch  angle  leg  should  be  used  against  the 
web. 

Flange  plates  such  as  14"Xl"  or  15"  1%"  may  be  made 
up  of  two  or  more  plates  as  2  14"  XH"  plates  or  3 
15"xV2'r  plates. 


Usually  one  top  flange  plate  is  made  nearly  or  quite  the 
full  length  of  the  girder.  The  theoretical  length  of  the 
other  flange  or  cover  plates  may  be  found  by  the  follow- 
ing formula: 

Total  flange  area  Area  of  cover  plate 


Square  of  span  in  feet      Square  of  length  of  cover  plate 
To  this  theoretical  length  of  the  cover  plate  add  a  foot 
or  more. 

This  formula  applies  as  stated  for  the  outside  cover 
plate.  For  the  second  cover  plate  substitute  for  "area  of 
cover  plate"  the  area  of  the  first  plus  the  second;  for  the 
third  cover  plate  this  "area  of  cover  plate"  is  the  area  of 
the  first  three,  etc. 

TABLE  V. 

RIVET  PITCH  IN  FLANGES  OF  GIRDERS  FOR  VARIOUS  UNIT  SHEARS. 

On  basis  of  bearing  value  of  rivets  at  18,000  Ibs.  per 
sq.  in. 


Unit  Shear 

8000 

7000 

6000 

5000 

4000 

3000 

2000 

2/4 

Rivets  
Rivets  
'  Rivets  

1.97 
1.69 

1.41 

2 
1 

1 

.25 
.93 
.61 

2 
2 
1 

.63 
.25 
.88 

3, 
2, 
2 

,15 
,70 

.25 

3.94 
3.38 
2.81 

5.25 
4.50 
3.75 

7.87 
6.75 
5.62 

The  rivet  spacing  in  the  flange  angles  for  rivets  through 
the  web  may  be  found  by  Table  V,  by  determing  first  the 
shear  per  sq.  in.  in  the  web.  The  closest  spacing  is  re- 
quired near  the  ends  of  span,  and  near  the  middle  of  span 
the  spacing  reaches  a  maximum,  which  is  generally  six 
inches.  A  few  different  spaces  will  be  employed,  using 
the  closest  for  a  few  feet  at  the  ends,  then  stepping  up  at 
intervals  to  the  maximum. 

The  thickness  of  the  web  plate  should  not  be  less  in 
any  case  than  about  1/200  of  the  clear  depth  between  the 
flange  angles,  as  thin  wide  plates  are  apt  to  have  buckles 
due  to  cooling,  which  are  very  hard  to  remove. 

84 


TABLE  VI. 


SHEAR    ON     PLATE    GIRDER     WEBS. 


d   [Allowed  Shr. 
T   |  per  Sq.  In. 

1 
t 

Allowed  Shr. 
per  Sq.  In. 

d   |  Allowed  Shr. 
t~  |  per  Sq.  In. 

40 
50 
60 

70 

7830 
6550 
5450 
4560 

80 
90 
100 
120 

3830 
3240 
2770 
2070 

140 
160 
180 

200 

1590 
1260 
1020 
840 

d=either  clear  depth  between  flange  angles  or  clear  dis- 
tance between  stiffeners. 

t=thickness  of  web. 

When  the  thickness  of  web  plate  is  relatively  less  than 
that  shown  in  Table  VI,  stiffeners  are  needed.  Thus,  sup- 
pose a  H-in-  girder  web  is  40  in.  between  flange  angles  in 
clear  depth  and  is  subject  to  5,000  Ibs.  per  sq.  ft.  of  shear. 
The  ratio  of  depth  to  thickness  is  here  107.  By  Table  VI 
a  shear  of  about  2,500  Ibs.  per  sq.  in.  is  allowed.  Stiffeners 
are  needed.  At  5,000  Ibs.  per  sq.  in.  a  ratio  of  depth  to 
thickness  of  65  is  allowed  This  would  require  about  24 
in.  in  the  clear  between  stiffeners.  A  pair  of  stiffener 
angles  should  then  be  used  about  two  feet  from  the  end 
of  girder.  If  the  shear  at  this  stiffener  is  less  than  at 
the  end  of  girder,  'the  space  to  the  next  stiffener  will  be 
more.  At  the  section  where  the  shear  is  2,500  Ibs.  per 
sq.  in.  no  stiffeners  are  required.  If  this  were  a  uniform- 
ly loaded  girder,  no  stiffeners  would  be  required  in  the 
middle  half.  One  quarter  of  the  girder  at  each  end  would 
need  stiffeners  varying  in  clear  spacing  from  24  in.  at  the 
ends  of  span  to  40  inches. 

The  end  stiffeners  of  a  girder  have  an  office  to  per- 
form which  is  more  than  the  mere  stiffening  of  the  web. 
They  should  be  designed  to  take  the  full  end  reaction  of 
the  girder  and  transmit  it  into  the  web.  A  unit  stress  of 
about  15,000  Ibs.  per  sq.  in.  may  be  used  in  determining 
the  area  required.  Thus  suppose  the  end  reaction  of  a 
girder  is  240,000  Ibs.  At  15,000  Ibs.  per  sq.  in.  this  would 
require  16  sq.  in.  in  the  angles.  This  could  be  made  up 


85 


of  4  angles  5x3^x1/&.  These  four  angles  must  deliver 
the  load  of  240,000  Ibs.  to  the  web  of  the  girder.  At  18,- 
000  Ibs.  per  sq.  in.  the  bearing  value,  say  of  a  %-in.  rivet 
in  a  ^-in.  web.  is  7880  Ibs.  Thirty  rivets  are  required, 
or  15  in  each  pair  of  angles. 

Examples : 

(1)  Given  a  girder  of  40  ft.  span  carrying  a  load  of 
3,000  Ibs.  per  ft.  The  total  load  on  the  girder  is  60  tons. 
Q  is  40X60=2,400.  By  Table  IV  a  girder  having  a 
30"x^"  web,  6"x6"x^"  flange  angles  and  a  14"x%" 
cover  plate  will  suffice,  if  the  web  plate  is  in  one  piece  or 
spliced  for  bending.  The  end  shear  is  3,000x20—60,000 
Ibs.  On  the  30"x^"  web  this  is  5,330  Ibs,  per  sq.  in.  By 
Table  V  the  rivet  spacing  of  24"  rivets  should  be  about 
2.5"  near  the  ends.  By  Table  VI  the  clear  depth  of  web 
may  be  60  times  the  thickness,  which  is  22.5" ;  as  the  clear 
depth  here  is  30 — 12  or  18",  no  intermediate  stiffeners  are 
needed.  The  end  stiffeners,  for  the  reaction  of  60,000  Ibs., 
require  60,000-1-15,000  or  4  sq.  in.  On  account  of  the  6" 
flange  angles  the  stiffener  angles  should  not  be  less  than 
say  2  angles  5"X31/&"X<H$",  which  would  be  more  area 
than  necessary.  For  the  length  of  the  cover  plate,  the 
total  flange  area  is  1.41  (^  of  web)  +11.50  (angles) +7 
(cover  plate)  =  19.91  sq.  in. 

By  the  formula 

19.91  7 


40X40  Square  of  length. 

from   which  the  theoretical  length   is  23.7   ft.     The  plate 
would  be  made  25  feet  long. 

Other  girders  could  be  selected  that  would  be  more 
economical  than  the  one  chosen.  For  example,  by  inter- 
polation it  is  seen  that  a  girder  with  a  32"x5-16"  web' 
6"x4"x7-16"  angles  and  a  13"x^4"  cover  plate  would  do. 
The  web  of  this  girder  'need  not  be  spliced  for  bending, 
since  Qi  is  used.  The  shear  on  the  web  is  6,000  Ibs.  per 
sq.  in.,  and  this  would  require  rivet  spacing  of  2*4",  which 
is  the  minimum  limit  for  a  single  row. 

86 


(2)  Given  a  girder  of  18  ft.  span  and  having  a  con- 
centrated load  at  its  center  of  10,000  Ibs.  A  concentrated 
load  at  the  center  of  a  girder  is  equivalent,  so  far  as  bend- 
ing is  concerned,  to  a  uniformly  distributed  load  of  double 
the  amount.  The  equivalent  uniform  load  on  this  girder 
is  then  20,000  Ibs.  or  10  tons.  Q  is  18X10=180.  By  Table 
III  the  girder  could  have  an  18"x*4"  web  and  3"x2^"x}4" 
flange  angles.  The  shear  is  5,000  Ibs.  or  1,100  Ibs.  per  sq. 
in.,  which  is  low. 


86o° 

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o 

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0 

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5 

o 

o 

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3 

0 

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Fig  5. 


Fioj.7 


End  stiffeners  should  be  turned  as  shown  in  Figs.  4 
and  6  and  not  as  in  Figs.  5  and  7.  In  the  latter  case  the 
outstanding  legs  of  angles,  which  take 'the  greater  part  of 
the  bearing,  are  over  ithe  edge  of  bearing  plate  and  end  of 
angles,  whereas  they  should  be  well  back. 

Where  there  is  a  heavy  concentrated  load,  such  as  a 
column,  supported  by  a  girder,  the  stiffener  under  the 
same  must  be  designed  to  take  the  column  load.  The  sec- 
tional area  and  the  rivets  in  the  web  may  be  found  as  for 
end  stiffeners,  as  illustrat?^  above. 

The  bearing  plate  of  a  gt><iet  /esting  on  a  wall  must  be 
designed  to  give  a  pressure  not  to  exceed  certain  limits 
and  must  be  stiff  enough  in  itself  to  distribute  the  load 


87 


over   this   area.     The  standards  given   in  Table  VII   will 
suffice  for  ordinary  cases  of  rolled  beams. 

TABLE  VII. 

CARNEGIE    STANDARD    WALL    PLATES. 


Depth  of   Beam 

Size  of   Plate 

Weight 

24-in. 

16x  1x16 

73  Ibs. 

20-in. 

16x  1x16 

73  Ibs. 

18-in. 

16x  1x16 

73  Ibs. 

15-in. 

12x24x16 

41  Ibs. 

12-in. 

12x24x12 

31  Ibs. 

10     and     9-in. 

8x^x12 

17  Ibs. 

8     and     7-in. 

8x^x  8 

12  Ibs. 

6     and     5-in. 

6x^x  6 

5  Ibs. 

4     and     3-in. 

6x%x  6 

5  Ibs. 

Smaller  dimension  is  in  direction  of  beam  for  plates 
not  square. 

On  cut  stone  or  concrete  the  pressure  allowed  per  sq. 
in.  on  bearing  plates  may  be  taken  as  300  Ibs. ;  on  brick  in 
cement  mortar,  200  Ibs.;  on  brick  in  lime  mortar,  110  Ibs. 
These  values,  with  the  load,  will  determine  the  area  of  the 
bearing  plate.  The  length  of  girder  resting  on  the  wall 
will  limit  the  dimension  of  'the  plate  in  one  direction.  If 
the  size  of  plate  required  necessitates  projection  of  the 
plate  beyond  the  angles  of  the  girder,  this  projection 
should  not  be  too  great  for  the  thickness  of  the  plate. 
In  fact  <the  flange  angles  of  the  girder  are  not  always  suf- 
ficient to  stiffen  the  bearing  plate  to  their  edge.  It  may 
be  better  in  many  cases  to  take  the  distance  out  to  out  of 
stiffener  angles  as  the  stiffened  portion  of  the  bearing 
plate. 


.  9 


88 


In  Figs.  8  and  9  the  projection  p  should  not  exceed 
seven  times  t  for  bearing  plates  on  brick  walls  in  lime 
mortar;  it  should  not  exceed  five  times  t  for  brick  in  ce- 
ment mortar,  nor  four  times  t  for  cut  stone  or  concrete 
walls. 

In  special  cases  cast  shoes  or  steel  spreading  beams  are 
necessary  to  give  sufficient  bearing  against  the  wall  and 
to  have  sufficient  stiffness  at  the  same  time.  Cast-iron 
shoes,  as  in  Fig.  10,  may  be  made  with  p  equal  to  twice  t. 

BOX     GIRDERS. 

Box  girders,  composed  of  two  web  plates,  four  flange 
angles,  and  cover  plates,  are  often  used  in  buildings,  as 
under  walls  or  suporting  heavy  loads.  Table  VIII  gives 
a  number  of  such  girders  with  co-efficients  for  finding 
their  capacity.  These  are  also  figured  at  15,000  Ibs.  per 
sq.  in.  on  the  steel.  The  depth  back  to  back  of  angles  is 
*4  inch  greater  than  the  depth  of  web.  The  size  of  rivet 
assumed  is  ^  in. 

The  spacing  of  rivets  in  'the  flanges  of  a  box  girder  is 
not  so  simply  determined  as  in  the  case  of  a  plate  girder, 
since  single  shear  on  the  rivet  generally  determines  its 
value  and  not  bearing.  But  as  there  are  two  rows  of 
rivets  to  rely  upon,  ordinary  close  spacing  will  be  ample. 
To  find  the  rivet  spacing  required  for  any  given  shear, 
divide  this  shear  by  >the  depth  of  the  girder  in  feet.  (In 
exact  work  it  should  be  the  effective  depth  or  the  dis- 
tance between  the  centers  of  gravity  of  the  flanges,  but 
the  depth  of  web  is  close  enough  for  ordinary  work.) 
Then  divide  this  shear  per  foot  by  the  single  shear  value 
of  one  rivet.  This  quotient  is  the  number  of  rivets  re- 
quired in  one  foot  along  the  flange.  In  the  case  of  a  box 
girder  these  rivets  are  in  two  rows.  Thus,  suppose  a  30" 
girder  has  an  end  shear  of  60,000  Ibs.  The  shear  per  foot 
is  60,000-^-2.5=24,000  Ibs.  The  value  of  a  $4 -in.  rivet  in 
single  shear  at  9,000  Ibs.  per  sq.  in.  is  3,980  Ibs. ;  24,000-h 
3,980=6  rivets  per  ft.  In  two  rows  this  would  require 
4-inch  spacing. 


TABLE   VIII. 


Capacity  of  Box  Girders, 

Unit  stress  15,000  Ibs.  per  sq.  in.     All  Dimensions 
in  inches. 


Angles 


No    | 

CVr  Part   |  */8  of 

Plate  IW'b  ofW'bl   Web 
|  Inc.  in  I  Inc.  in 
j  Flngs.  |  Flngs. 


3  x3 
3  x3 
3  x3 


12x34 
12x34 


"R  I  813!  1038 
4  I  1299J  1527 
™  I  1587J  1811 


3     x3     xft|12xf$|  «{•    |  1018|  1369 

3  x3     x-ft  1 12x34 1  H  1620|  1974 

4  x3     x^  1 12x3/|  ro    |  i987[  2337 

3^x3^x3/6112x3^1  ,«   |  11951  1545 

3^x3 1^x3^  1 12x34  |  x    |  1799|  2150 

3^x3^x14112x341  %    |  2319|  2669 


3^x3^x3^112x3/61  "V,  |  1440] 

3^x3^x1^112x14!  £  2159| 

3j/2x3!/3xi4ll2x3/,|  n  I  2792| 

4     x4     x  3^|  12x3/61  -R  |  1563| 

4     x4     x 3/6  1 12x34  X  |  2284| 

4'     x4     x 34  1 12x34  £  |  3035| 


4  x4  x  3^  |12x^ 
4  x4  xH  |12x34 
4  x4  x  341  12x34 


3     x3 

3     x3     xa^  |18x34 
3     x3 


1830! 
2667| 
3553J 


1946 
2666 
3297 

2070 
2791 
3541 

2518 
3354 
4240 


1437| 
2382| 
2679| 


1788 
2736 
3031 


3  x3  x3/6|18x^|  «R  I  17271  2137 
3  x3  x3^|18xi4|  x  I  28551  3366 
3  x3  xH 1 18x34 1  ^  |  3214|  3723 


3^x3^x3^118x3/6  | 


1850) 
2989! 
3620| 


2358 
3498 
4126 


18x34|     x    | 
3^x3^x34  18x34J    5?    I 


2162! 
3484| 

4227| 


2850 
4172 

4915 


4  x4  x?^  1 18xi^  |  -B  |  2308|  2996 
4  x4  xi^|18xi4|  *  I  3630|  4321 
4  x4  xi4|18xi4|  ^r  [  4516|  5205 


4     x4 

46  x4     x^|  18x34 
4     x4 


2643 
4148 
51691 


3545 
5052 
6070 


Angles 


CVr 
Plate 


Part   |  y8  of 
W'b  |  of  W'b  |   Web 
Inc.  in  Inc.  in 
Flngs.    Flngs. 


..      .       .     122x34 
3^x3^x14122x341 


^  !  2743|  3431 
x  I  4390J  5080 
^  I  4870|  5560 


x3/8  ! 
22x34| 


3139| 

5014| 
5567| 


4041 
5918 
6470 


4     x4 

4  x4  x}i  |22x34l 

4  x4  xi4  |22x34| 


j.  3006| 
x  48811 
»  5902[ 


3908 
5785 
6804 


4  x4  x3^|  22x3/8  1 
4  x4  x 
4  x4  xa 


<-«>  3386| 
^  5489| 
%  6644  1 


4525 
6630 
7782 


*,  4122| 
K  6806| 
*  7454| 


5261 
7950 
8593 


3^x3Kx34|24x%| 


|  4583| 
|  75581 
|  8280| 


5986 
8967 
9685 


4  x4 
4  x4 
4  x4 


|  4867| 
i  78601 
|  8700| 


6269 
9270 
10110 


4  x4  xy2  24xT7R| 
4  x4  x^  1  24x7^| 
4  x4 


5357| 
I  8640| 
|  9570| 


7"058 
10350 
11280 


6     x6 
6     x6 

6     x6     x34|30xl 


6     x6     x 

6     x6     xH  30x1 

6     x6     x34|30xl 


6     x6     xy2\ 

6     x6     xj^|36xl 

6     x6     xi4|36xl 


6  x6 
6  x6 
6  x6 


;^|36xl 
:34|36xl 


•-§0  I  8240| 
x  I  133101 
S  I  14790| 


10540 
15600 
17080 


v£  I  9440| 
X  I  15200 
§  I  16910! 


12430 
18200 
19910 


sa 


11990| 
19840| 
21770] 


17050 
24900 
26840 


13330]  19580 
220401  28290 
241901  30440 


Examples : 

(1)  Given  a  floor  girder  of  30  ft.  span,  to  be  limited  in 
depth  to  about  24  inches,  the  total  load  being  3,600  Ibs. 
per  ft.    The  load  in  tons  is  1.8X30=54.    Q  is  54X30=1620. 
A  box  girder  with  24"x5-16"  webs,  3"x3"x^"  angles  and 
12"xM"    cover   plates   will    suffice.     The    angles   could   be 
9-16"  thick,  if  the  web  plates  are  in  one  piece. 

(2)  Given  a  box  girder  on  a  60-foot  span  supporting  a 
24-inch    wall,    the    total    load     per    ft.    being    5,000     Ibs. 
The     load     carried     is     5,000X60=300,000     Ibs.     or    150 
tons.     Q    is    150X60=9,000.     By   Table    VIII    it    is     seen 
that    a    box    girder    with    two    66"x5-16"    webs    4"x4"x^" 
angles    and    24"x^"    cover    plates    would    do.      The    web 
plates  need  not  be  spliced  for  bending,  as  .Qi  is  used,  but 
of   course    they    should   be    spliced    for    shear.      The    end 
shear  of  this  girder  is  150,000  Ibs.     On  the  two  56"x5-16" 
webs  this  is  3,640  Ibs.  per  sq.  in.    The  webs  need  stitfeners. 
These  should  be  spaced,  according  to  Table  VI,  about  83 
times  the  thickness  of  the  web  in  the  clear  or  26  inches 
at   the   end   of  girder.     At  quarter  points   the   spacing  of 
stiffeners  is  about  40  inches;  etc.     For  flange  rivets,  the 
shear  per  foot  at  end  of  span  is  150,OOQ-=-5. 5=27,500  Ibs. 
At  3,980  Ibs.  per  rivet  6.9  rivets  are  required  per   ft.  or 
3.5"  spacing  in  each  of  the  two  rows. 

Box  girders  should  have  occasional  inside  diaphragms 
composed  of  a  plate  and  angles  riveted  to  the  v/ebs 
These  are  quite  necessary  where  the  load  is  applied  to 
one  side  of  the  girder,  so  as  to  insure  the  uniform  distri- 
bution of  it  he  load  into  the  two  sides  of  the  girder.  A 
diaphragm  could  take  the  place  of  a  pair  of  stiffener 
angles  in  a  deep  girder. 

Box  girders  are  sometimes  used  as  cantilever  girders 
in  foundation  work  to  support  wall  columns  that  must 
have  their  foundation  located  back  from  the  center  of 
the  column.  In  such  case,  to  use  Table  VIII  the  bending 
moment  in  the  girder  should  be  found  in  foot-pounds  and 
this  moment  divided  by  250,  which  will  give  an  equivalent 
of  Q  in  the  table. 

91 


Example  of  cantilever  girder. 

Given  a  cantilever  girder  supporting  a  column  having  a 
load  of  120,000  Ibs.,  the  overhang  being  5  ft.  The  bend- 
ing moment  is  120,000X5=600,000  ft.-lbs.  Dividing  this 
by  250,  Q  is  found  to  be  2,400.  By  Table  VIII,  interpolat- 
ing, it  is  found  that  the  girder  could  be  composed  of  2 
webs  42"x5-16",  4  angles  4"x4"xH",  and  2  plates  12"xK,,. 


92 


CHAPTER  VIII. 
Trusses. 

The  designing  of  a  truss  involves  first  the  calculation 
of  the  stresses  in  the  several  members  and  the  selection  of 
suitable  members  to  take  these  stresses.  The  bending 
stresses  as  well  as  the  direct  stress  must  be  found  for  any 
members  subject  to  transverse  loading,  and  such  members 
must  be  designed  to  resist  both  kinds  of  stress.  The 
end  connections  of  all  members  must  be  detailed  so  that 
they  will  be  capable  of  taking  the  full  stress  of  the  mem- 
bers, and  the  truss  must  be  braced  against  lateral  dis- 
placement both  as  a  whole  and  locally  so  that  compres- 
sion members  that  are  considered  of  certain  free  lengths 
in  the  general  design  will  be  supported  at  these  limits  of 
length.  In  general  truss  members  should  be  symmetrical 
about  the  plane  of  the  truss,  and  the  lines  through  the 
centers  of  gravity  of  the  several  members  meeting  at  a 
common  point  should  intersect  in  a  common  point. 

Persuant  of  the  author's  intention  to  cover  in  this  book 
only  simple  designing,  this  chapter  will  take  up  only  the 
design  of  simple  trusses  and  simple  methods  of  finding 
the  stresses  in  the  same. 

Plates  I  to  III,  inclusive,  give  co-efficients  on  the  sev- 
eral truss  members  by  which  the  stresses  in  these  mem- 
bers may  be  found.  The  condition  is  that  of  a  simple 
truss  resting  on  walls  and  not  of  a  truss  acting  to  brace 
a  building  through  the  medium  of  knee  braces.  The 
trusses  are  further  symmetrically  loaded  and  not  subject 
to  unusual  loads,  such  as  suspended  galleries,  etc.  To 
find  the  stress  in  any  member  compute  the  total  load  that 
a  truss  must  carry;  then  multiply  this  by  the  co-efficient 
on  the  member  in  which  the  stress  is  desired. 

The  minus  sign  stands  for  compression,  and  the  plus 
sign  stands  for  tension. 

93 


As  indicated  on  Plate  III,  these  same  diagrams  may  be 
used  to  find  the  stresses  in  a  lean-to  truss,  that  is,  a  truss 
of  the  shape  of  half  of  one  of  these.  The  stresses,  for  the 
same  panel  loads,  will  be  the  same  for  the  half  truss  as 
for  the  full  truss  for  all  members  except  the  horizontal 
member  or  the  bottom  chord  and  'the  long  inclined  mem- 
ber or  the  top  chord.  The  "total  load"  for  a  lean-to  truss 
is  of  course  the  load  that  the  full  truss  would  carry  and 
not  the  load  on  the  half  truss.  The  co-efficient  for  each 
member  of  the  bottom  chord  is  reduced  by  .375,  .433,  etc., 
for  the  several  pitches.  It  is  seen  that  these  are  the 
stresses  of  the  middle  portion  of  this  chord,  which,  of 
course,  has  a  nominal  stress  when  the  truss  is  supported  at 
the  peak.  (By  using  the  term  nominal  it  is  meant  to 
convey  that  there  is  no  calculable  stress  in  the  member  in 
question.)  The  top  chord  stress  in  the  half  trusses  will 
be  reduced  throughout  by  the  amounts  given  on  Plate  III. 

Plates  IV  to  VIII,  inclusive,  give  the  stresses,  in  terms 
of  the  panel  loads  P  and  the  lengths  of  members,  for 
trusses  with  parallel  chords.  The  panel  load  for  a  four- 
panel  truss  is  one-quarter  of  the  total  load  carried  by  the 
truss;  that  for  a  five-panel  truss,  one-fifth;  etc.  At  each 
end  there  is  of  course  a  half  panel  load.  It  is  seen  that 
these  stresses  are  worked  out  on  the  assumption  that  the 
full  load  is  applied  at  the  top  chord.  If  the  load  or  any 
part  of  it  is  applied  at  the  bottom  chord,  the  compres- 
sion in  all  vertical  members  will  be  diminished  by  just 
the  amount  of  the  panel  load  that  is  transferred  to  the 
bottom  chord,  (or  the  tension  in  the  verticals  will  be 
increased  by  that  amount)  ;  the  stresses  in  diagonal  mem- 
bers and  chords  will  not  be  affected. 

The  stresses  in  Plates  IV  to  VIII,  inclusive,  are  for 
uniform  load  on  the  trusses;  that  is,  they  are  for  the  or- 
dinary case  of  roof  trusses  carrying  their  full  load  and 
not  subject  to  unsymmetrical  loading.  These  diagrams 
would  not  apply  to  floor  trusses,  where  the  full  load  may 
not  be  applied  uniformly;  for,  while  they  would  give  the 
maximum  chord  stresses,  the  web  stresses,  particularly 

94 


near  the  middle  of  truss,  would  be  quite  different  under 
partial  loading  with  the  same  panel  loads. 

Plate  IX  shows  the  method  of  finding  graphically  the 
stresses  in  a  common  form  of  roof  truss,  whose  upper 
chord  is  sloped.  In  this  example  the  stress  computation  L 
simplified  by  omitting  in  the  diagram  loads  3,  5,  and  7  and 
concentrating  the  roof  loads  at  2,  4,  6,  and  8.  The  graphic 
diagram  is  made  as  though  the  vertical  members  of  the 
truss  were  omitted.  Members  2-11,  4-13,  etc.,  would  have 
nominal  stress.  Members  3-12,  5-14,  etc.,  would  have  a 
compression  equal  to  the  panel  load  at  3. 

Very  frequently  graphical  computation  of  stresses  may 
be  greatly  simplified  and  expedited  by  assuming  some  un- 
important members  to  be  absent.  The  stresses  in  ithe 
main  members  are  not  greatly  affected  by  this  short-cut. 

The  method  of  proceedure  in  finding  by  the  graphical 
method  the  stresses  in  a  truss  is  as  follows: 

First  find  the  panel  loads,  and  mark  the  same  on  the 
'diagram.  Then  find  the  reactions,  and  mark  these  on  the 
diagram.  In  the  case  shown  on  Plate  IX  the  panel  loads 
are  the  vertical  forces  shown  at  2,  4,  6,  and  8. 

(Note  that  loads  2  and  8  are  \l/2  single  panel  loads  and 
4  and  6  are  equal  to  two  single  panel  loads.) 

The  reactions  are  the  forces  shown  at  10  and  18.  Or- 
dinarily the  reactions  are  each  equal  to  one-half  the  sum 
of  the  panel  loads. 

The  next  step  is  to  letter  the  diagram  of  the  truss. 
This  is  done  by  placing  a  letter  below  the  truss,  then  at 
the  ends  of  truss  and  between  the  panel  loads,  then  in 
each  triangle  making  up  the  frame  of  the  truss.  The 
object  in  this  lettering  is  to  make  it  possible  'to  designate 
any  member  or  force  by  naming  two  letters,  one  on  each 
side  of  that  member  or  force.  Thus,  in  passing  from 
the  space  A  to  the  space  B  the  reaction  at  the  left  end 
of  truss  will  be  crossed;  that  reaction  is  then  the  force 
AB;  in  passing  from  space  B  to  space  C  the  panel  load 
at  2  is  crossed;  that  panel  load  is  then  BC;  in  passing 
from  space  M  to  space  L,  the  member  12-4  is  crossed;  that 

95 


member  then  ML,  etc.  The  significance  of  this  lettering 
of  the  spaces  can  best  be  understood  by  a  study  of  the 
subsequent  processes. 

The  next  step  is  to  make  a  diagram  of  the  applied  loads. 
These  loads  are  the  two  reactions  and  the  several  panel 
loads.  These  are  drawn  to  scale.  In  the  example  on 
Plate  IX,  BA  is  the  left-hand  reaction  and  AF  is  the 
right-hand  reaction.  FE,  ED,  DC,  and  CB  are  the  several 
panel  loads.  The  arrows  indicate  the  direction  of  these 
forces.  If  the  reaction  AB  is  25,000  Ibs.,  the  line  AB  in 
the  stress  diagram  will  be  made  25  units  in  length  on 
some  suitable  scale.  All  stresses  and  forces  will  be  laid 
out  or  measured  on  this  same  scale. 

The  stress  diagram  is  then  completed  in  the  following 
manner.  Beginning  at  either  end  of  the  truss,  as  at  the 
right  end,  a  line  is  drawn  from  A  parallel  to  the  member 
AG  (or  16-18)  ;  then  a  line  is  drawn  from  F  parallel  to 
FG  (or  8-18).  The  intersection  of  these  lines  is  marked  G. 
The  length  of  the  line  FG,  measured  on  the  chosen  scale, 
is  the  stress  in  the  member  FG,  and  the  length  of  AG  is 
the  stress  in  member  AG  -n  the  former  is  compression,  and 
the  latter  is  tension,  as  indicated  by  the  minus  and  plus 
signs  on  the  members.  Lines  EH  and  GH  are  drawn 
parallell  to  their  respective  members,  locating  the  point 
H.  Then  HJ  and  AJ  are  drawn ;  then  JK  and  DK ;  then 
KL  and  AL;  then  LM  and  CM;  then  MN  and  BN.  If 
the  final  line  BN  is  found  to  be  parallel  with  member  2-10 
the  polygon  is  said  to  "close."  This  is  evidence  that  the 
work  is  correct.  The  diagram  could  have  been  worked 
up  from  both  right  and  left  ends  of  the  truss  at  the  same 
time,  as  by  drawing  AN  and  BN,  NM  and  CM,  etc.  The 
closing  line  would  then  be  one  of  the  short  lines  about 
L,  K,  and  J.  All  of  the  stresses  in  the  members  arc  found 
by  scaling  this  diagram. 

In  order  to  find  the  sign  of  a  stress  proceed  as  follows: 
Select  a  point,  as  4,  and  trace  the  diagram  of  the  forces 
meeting  at  this  point.  This  diagram  is  CDKLM.  If  the 
direction  of  one  of  these  forces  is  known,  the  direction 


or  sign  of  the  others  may  be  found  thus.  In  this  case 
the  direction  of  CD  is  known,  that  is,  this  force  is  down, 
or  toward  the  point4.  Following  the  diagram  around 
in  this  direction  the  next  force  is  CM,  which  is  in 
the  direction  of  the  arrow,  or  toward  point  4.  The 
next  force  is  ML,  which  is  also  toward  point  4.  The  next 
force  around  the  polygon  is  LK,  which  is  downward  to  the 
right  or  away  from  point  4.  KD  is  toward  point  4.  All 
the  members  that  can  be  replaced  by  forces  toward  point  4 
are  in  compression.  LK  or  the  force  away  from  point  4, 
is  in  tension.  In  this  manner  the  sign  of  any  of  the 
stresses  can  be  found.  It  is  necessary  to  try  only  a  few 
points.  The  top  chords  will  be  in  compression  and  the 
bottom  chords  will  be  in  tension. 

As  in  the  case  of  the  previously  mentioned  trusses  the 
diagram  of  Plate  IX  is  for  uniform  loading.  However 
the  method  may  be  applied  to  find  the  stresses  for  any 
sort  of  loading.  If  the  loading  is  unsymmetrical,  the  re- 
actions will  not  be  equal.  These  reactions  may  be  calcu- 
lated by  taking  moments  around  either  support.  The  clos- 
ing of  the  polygon  of  forces  will  check  the  correctness  of 
the  reactions  as  well  as  other  parts  of  the  work. 

Plate  X  shows  another  style  of  roof  truss  and  the 
graphical  solution  of  the  stresses  in  the  same.  The  meth- 
ods are  the  same  as  for  Plate  IX.  Note  that  the  top  chord 
of  this  truss  is  member  3-5.  Members  3-4  and  4-5  act 
merely  as  supports  for  the  panel  load  at  4.  The  diagonals 
in  the  middle  quadrilateral  have  nominal  stress. 

Plate  XI  shows  a  truss  similar  in  shape  to  that  on 
Plate  X  and  a  simplified  method  of  finding  the  stresses 
in  the  main  members.  The  applied  loads  are  here  con- 
centrated at  2  and  3.  If  there  are  other  members  than 
these  main  members,  they  may  be  light  enough  to  need 
no  special  calculation. 

Plates  XII  and  XIII  show  a  detailed  and  a  simplified 
method  of  finding  the  stresses  in  'the  truss  shown,  as  also 
Plates  XIV  and  XV. 

Plate  XVI  shows  still  another  common  form  of  roof 
truss  and  the  graphical  solution  of  the  stresses. 

97 


PLATE  i 
STRESSED    IN   ROOF  TRUSSES 


TOTAL  LOAD  ON  TRUSS 
-  UNITY 


PLATE.  II 
5TR.E5SE5     IN    R.OOF  TR.US5Ev5 


SPAN 


PLATE    III 
STR.E55ES     IN    R.OOF  TRUSSED 


SPAN 


TOTAL  LOAD  ON  TRUSS  is  UNITY 

FOR   A   LEAN-TO  (ONE- HALT  or  ANY  OF  THESE  TRUSSES) 

THE    WEB     STRESSES  ARE   SAME   AS  GIVEN    IN   FI6S 

.451  © 

TOP  CHORD  STRESS  is  DEDUCED  BY.    .  500©  BoTrCHof?D.433@ 

.  .  559©  STRESS  BY  .« 
.673$) 


100 


PLATE  IV 

TRUSSED    WITH 
PARALLEL  CHORDS 


PLATE  V 

TRU55E5  WITH 
PARALLEL  CHORDS 


f  r 


^ 


^    1^ 


•* 


Lr-UirJ-r- 


2"  .E          P          P          P         P 

-7-     £—      i-g  l-g  1 

J} 


/ 


^4-r-ir 


~f 

-£! 

I 


L 

I  X 


101 


PLATE  VI 
TR.US5E5    WITH   PARALLEL  CHORDS- 


I   ' 


»«,    -4B,     - 

2R  it        . 


102 


PLATE   Vll 
TRUSSED     WITH    PARALLEL    CHORDS 


Up 


IDS 


PLATE.    VIII 
TRUSSES     WITH    PARALLEL 


r  r  r 


r#  r*  +i$  • 

— r-^-r+-r  +  r-ir-r-+-  PH^P^ 


104 


PLATE    IX 


10  +     II      +    £    +    •    +    H     +    0    >     1C    ••*     Y    +    « 


105 


PLATLX 


106 


PLATE.  XI 

.7 


107 


108 


PLATLXIJI 


109 


PLATE  XIV 


110 


PLATtXY 


111 


112 


TENSION    MEMBERS. 

In  riveted  trusses  light  tension  members  are  usually 
made  of  angles,  single  or  double.  Flats  are  sometimes 
used,  but  they  are  troublesome  in  a  truss,  because  they  are 
apt  to  be  buckled  when  the  truss  is  riveted  up. 

When  a  single  angle  is  used  in  tension,  its  effective  area 
should  be  counted  as  'the  area  of  one  leg  only  of  the  angle. 
Thus,  a  3"x3"x^"  angle  would  be  counted/  as  though  it 
were  a  3"x^$"  flat,  a  5"x3^z"x%"  angle  would  be  counted 
as  a  5"x^"  flat,  etc.  This  is  to  compensate  for  the  lack 
of  symmetry,  or  the  eccentric  application  of  the  stress,  and 
the  consequent  bending  stress  in  the  member. 

A  member  composed  of  two  angles  symmetrically  placed 
with  respect  to  the  plane  of  the  truss  does  not  have  the 
bending  stress  mentioned  in  the  last  paragraph.  How- 
ever such  angle  is  not  good  in  tension  for  its  full  sec- 
tional area.  The  available  area  of  the  angle  is  reduced  by 
the  punching  away  of  metal  for  rivet  holes. 


Fig.  I. 

It  is  seen  that  at  section  AA,  Fig.  1,  the  area  of  metal  in 
tension  is  equal  to  the  full  area  of  the  angle  less  the  prod- 
uct of  the  thickness  of  metal  by  the  diameter  of  the  rivet 
hole.  In  practice  this  diameter  of  the  rivet  hole  is  as- 
sumed to  be  I/s"  greater  than  the  nominal  diameter  of 
the  rivet.  It  is  also  seen  that  if  the  hole  in  the  other 
flange  of  the  angle  is  near  the  section  AA,  the  net  area 
through  a  zig-zag  line  cutting  both  holes  may  be  less 
than  through  the  square  section  cutting  one  hole  only.  In 
detailing  tension  members  care  must  be  taken  to  see  that 
the  minmum  number  of  rivet  holes  occur  at  or  near  any 
given  transverse  section.  Angles  having  three  or  four 
rows  of  rivets  (as  6"x31/£"  and  6"x6"  angles)  usually  have 
two  rivet  holes  deducted  in  the  net  section. 

113 


IK  channel  sections  in  tension  one  or  more  rivet  holes 
will  be  deducted,  depending  on  the  deail  of  'the  member. 
If  the  member  has  lattice  or  batten  plates,  that  is,  if  the 
flanges  are  punched,  two  flange  holes  will  be  deducted 
from  the  gross  area  and  as  many  web  holes  as  occur  in 
the  same  transverse  section. 

Eye-bars  and  rods  with  loops  at  the  ends  are  designed 
for  tension  in  the  full  section  of  the  bar  or  rod,  as  the 
eye  or  loop  is  made  capable  of  taking  the  full  value  of  the 
bar  or  rod. 

Bolts  or  rods  with  either  plain  nuts  or  clevis  nuts  at 
the  ends  are  designed  for  tension  in  the  full  section  of 
the  bolt  or  rod,  provided  the  threaded  ends  are  upset.  I£ 
the  threaded  ends  are  not  upset,  the  value  of  the  bolt  or 
rod  is  only  that  of  the  metal  in  a  circle  whose  diameter  is 
measured  at  the  root  of  the  threads.  Table  I  gives  the 
tensile  strength  of  rods  of  various  diameters,  the  area  be- 
ing measured  at  the  root  of  threads.  The  unit  used  in 
the  table  is  10,000  Ibs.  For  any  other  unit,  as  16,000  Ibs. 
per  sq.  in.  multiply  the  tabular  value  by  1.6,  etc.  The 
screw  threads  used  are  Franklin  Institute  Standard.  (See 
Godfrey's  Tables,  page  35.) 


TABLE  I. 

Tensile  Strength  of  Rods  at  10,000  Ibs. 
per  sq.  in.  Area  Measured  at  Root 
of  Threads. 

Dia.  of 
Rod 
in  In. 

Tensile 
Strength. 

Dia.  of 
Rod 
in  In. 

Tensile 
Strength. 

Dia.  of 
Rod 
in  In. 

Tensile 
Strength. 

M 

H 

1/8 
1% 

m 
i% 
IH 

m 
.1% 

3020 
4200 
5500 
6940 
8910 
10570 
12950 
15150 
17440 
20480 
23020 

2H 

2y4 
2% 

2y2 

2ti 

2H 

2H 

l*A 

z% 
ty* 

26500 
30240 
34210 
37160 
41550 
46180 
51070 
54290 
59570 
65100 
70900 

3^ 
3tt 
324 
3^ 
4 
4H 
454 
4M 
4^ 
4^ 
4^4 

75500 
81700 
86400 
93000 
99900 
107100 
113300 
120900 
127400 
135500 
142200 

114 


In  building  work  a  unit  stress  of  16,000  Ibs.  per  sq.  in, 
is  usually  allowed  on  rods  and  bars.  The  same  unit  is 
sometimes  allowed  on  the  net  section  of  shapes  such  as 
angles  and  channels,  though  15,000  Ibs.  is  preferable,  be- 
cause of  the  uncertain  effect  of  punching,  and  because 
stress  is  not  so  uniformly  distributed  in  shapes  as  in  rods 
and  bars. 

Examples : 

(1)  Required  the    section   of   a   tension   member   in    a 
light  truss  to  take  11,000  Ibs.  of  stress.     Here  the  area,  at 
15,000  Ibs.  is  .73  sq.  in.    The  area  of  one  leg  of  a  3"x2^"x 
YA!'  angle  is  .75  sq.  in.     This  could  be  used.     A  \Y%"  rod, 
not  upset  has  a  tensile  strength,  by  Table  I,  at  16,000  Ibs. 
per  sq.  in.,  of  11,100  Ibs.     This  rod  could  be  used,  if  the 
style   of   truss   permit. 

(2)  Required  the  section  of  a  member  to  take  a  tensile 
stress  of  35,000  Ibs.     The  net  area  required,  at  15,000  Ibs. 
per   sq.   in.,   is   2.33   sq.    in.     If   the   member    is   composed 
of  2  angles,  each  angle  will  have  a  net  area  of  1.17  sq. 
in.  or  a  gross  area,  adding  .33  sq.  in.  for  the  rivet  hole, 
of  about  1.50  sq.  in.    A  3"x3"xj/4"  angle  has  a  net  area  of 
1.44— .22=1.22  sq.  in.     (The  deduction  of  .22  is  for  a  H" 
rivet  hole  or  %x^4.)     Two  such  angles  could  be  used. 

(3)  Required  the   section   of   an   upset   rod   to  take   a 
stress  of  80,000  Ibs.     The  area,  at  16,000  Ibs.  per  sq.  in., 
is  5  sq.  in.     By  reference  to  a  table  of  the  area  of  rounds 
(Godfrey's  Tables,  page  61,  et  seq.)    it   is    found  that  a 
2  9-16"  round  rod  would  be  required.     If  two  rods  were 
used,  each   should  have  a  diameter  of   1    13-16." 

Tension  members  in  timber  trusses  are  usually  made  of 
steel  or  iron  rods,  though  the  bottom  chords  are  often 
made  of  wood.  The  section  required  is  usually  determined 
by  the  detail  at  the  ends  or  splices.  Wooden  members  do 
not  admit  of  very  efficient  details  for  tension.  A  large 
portion  of  a  wooden  tension  member  may  be  notched 
away  for  the  splice  or  bored  out  for  bolts.  A  tensile 
stress  of  1,200  Ibs.  per  sq.  in.  for  white  pine  and  1,600  Ibs. 

115 


per  sq.  in.   for  yellow  pine  or  white  oak  may  be  allowed 
on  ithe  net  section  of  the  wood. 

COMPRESSION      MEMBERS. 

The  selection  of  the  size  of  compression  members  in 
a  truss  should  be  carried  out  by  the  methods  of  Chapter 
IV.  Tables  IV  and  V  of  that  chapter,  as  stated  in  the 
chapter,  are  for  single  angles  as  members  having  square- 
ended  or  rigid  details.  In  an  ordinary  light  truss,  if 
a  single  angle  is  used  in  compression,  only  about  half  of 
the  value  shown  in  Tables  IV  and  V  should  be  used  as 
safe  values  of  the  members. 

Tables  VI  ito  IX,  inclusive,  of  Chapter  IV  may  be  used 
for  truss  members  without  any  reduction  of  the  tabular 
load. 

In  general  it  is  best  to  select  standard  angles  and  a 
small  number  of  different  sizes  for  any  given  truss. 

TRUSS    MEMBERS    IN    BENDING. 

Truss  members  are  sometimes  subject  to  transverse  or 
bending  stresses  as  well  as  direct  stress  ('tension  or  com- 
pression). Such  members  must  be  designed  for  both  bend- 
ing and  direct  stress,  the  unit  stress  in  the  steel  being  kept 
within  certain  limits. 

When  all  of  the  load  on  a  truss  is  cencentrated  in  beams 
'that  connect  to  the  truss  at  the  panel  points  only,  there 
will  be  no  bending  in  the  truss  members,  but  direct  stress 
only.  The  roof  load,  however,  is  very  frequently  dis- 
tributed uniformly  along  the  top  chord  of  a  truss  or  con- 
centrated in  beams  or  purlins  that  do  not  connect  to  the 
truss  at  panel  points.  The  top  chord  must  then  act  as  a 
beam  as  well  as  a  compression  member  and  must  be  de- 
signed accordingly.  A  member  suitable  for  this  condi- 
tion is  deep  vertically.  Examples  of  such  members  are. 
two  angles  of  unequal  legs  with  the  long  legs  vertical,  two 
channels,  two  angles  of  equal  legs  with  a  deep  plate  riv- 
eted between  them.  In  wooden  trusses  of  course  'the  mem- 
ber is  made  deeper  in  the  vertical  dimension  than  in  the 
horizontal. 

116 


There  is  much  variation  in  the  practice  of  designing 
members  under  combined  direct  and  bending  stress.  There 
is  also  very  frequently  little  attention  paid  to  the  neces- 
sity for  care  in  such  designing.  The  rigid  or  correct 
treatment  of  the  problem  will  not  be  given  here,  as  it  in- 
volves structural  engineering  principles  outside  of  the 
scope  of  this  book.  Approximate  methods  only  will  be 
given  here.  They  will  be  found  to  be  safe,  though  not 
wasteful ;  the  results  will  be  close  to  correct  theoretical 
methods  and  very  much  superior  to  the  guess-work  so 
often  resorted  to. 

WOODEN    TRUSS    MEMBERS    IN    BENDING. 

First  find  the  actual  or  equivalent  uniform  load  on  the 
member  by  the  methods  of  Chapter  VI.  Then  fmd  the 
value  of  C,  that  is,  the  product  of  the  uniform  load  by 
the  span  in  feet.  The  span  in  feet  is  the  horizontal  dis- 
tance between  the  panel  points  or  supports  of  the  member 
considered.  (It  is  not  the  inclined  distance  for  inclined 
members.)  Next  find  in  Table  I  of  Chapter  VI  a  section 
whose  value  C  is  greater  than  that  just  computed,  for  a 
trial  design.  Then  find  by  Chapter  IV,  using  Table  T, 
the  value  of  'this  member  in  compression.  Now  compare 
the  value  of  C  required  with  that  of  the  member  selected 
'as  also  the  actual  compression  'in  the  member  with  its 
allowed  compression,  and  add  these  two  ratios ;  they 
should  equal  unity.  Thus,  if  the  member  is  under 
7-10  of  its  allowed  bending,  it  may  carry  at  the  same  titre 
3-10  of  its  allowed  compression.  If  the  sum  of  the  ratios 
is  greater  than  unity,  select  a  heavier  or  deeper  member ; 
if  less  than  unity,  select  a  lighter  section. 
Examples : 

(1)  Required  the  section  of  a  rafter  five  feet  long  on 
the  slope  and  four  feet  in  the  horizontal  direction,  carry- 
ing a  load  of  400  Ibs.  per  horizontal  foot  and  subject  to 
10,000  Ibs.  of  compression.  In  this  case  C  is  400X4X4= 
6,400.  A4"x6"  in  white  pine  has  a  value  C= 12,800,  by 
Table  I,  Chapter  VI.  The  rafter  would  be  stayed  hori- 
zontally by  the  joists  resting  upon  it,  hence  the  unsup- 

117 


ported  dimension  would  be  six  inches.  The  ratio  of  this  to 
the  length  of  rafter  is  10.  By  Table  I,  Chapter  IV,  the 
allowed  unit  stress  for  this  ratio  is  820  Ibs.  per  sq.  in. 
The  member  is  then  good  for  a  compressive  stress  of 
820X24=19,680  Ibs.  The  member  is  thus  subject  to  .50 
of  its  allowed  bending  value  and  .51  of  its  allowed  com- 
pression. The  sum  of  these  two  is  1.01,  and  the  member  is 
therefore  correct. 

(2)  Required  the  isize  of  a  horizontal  chord  mem- 
ber 10  ft.  between  panel  points,  the  roof  load  being  600 
Ibs.  per  foot  and  the  compression  being  28,000  Ibs.  The 
roof  beams  are  five  feet  apart,  that  is,  at  panel  points  and 
midway  between  panel  points.  In  this  case  C=600XlOX 
10=60,000.  In  yellow  pine  a  4x16  piece  has  a  value 
C=l  13,770.  For  compression  the  unsupported  length  is 
5  ft.  and  the  width  is  4  in.  The  ratio  for  Table  I,  Chap- 
ter IV,  is  15  and  by  interpolation  the  unit  stress  is  found 
to  be  730  Ibs.  per  sq.  in.  The  allowed  compression  is 
730X4X16=46,720  Ibs.  The  bending  is  then  .53  of  the 
capacity  and  the  compression  .60.  This  gives  a  total  of 
1.13  which  is  more  than  the  limit.  The  member  could 
be  5"xl6",  or  by  trial  it  will  be  seen  that  6"xl4"  would 
be  somewhat  stronger  than  necessary.  This  could  be 
made  of  three  2"xl4"  pieces  spiked  or  bolted  together. 

STEEL,  TRUSS    MEMBERS    IN    BENDING. 

The  same  method  of  proceedure  would  be  used  for 
steel  members  as  for  wooden  members  except  that  the  load 
is  found  in  tons  and  Q  instead  of  C  thus  found. 

Examples : 

(1)  Required  the  section  of  a  top  chord  member  4  ft. 
long,  the  compression  being  75,000  Ibs.  and  the  load  per  ft. 
on  the  chord  1,000  Ibs.  Here  the  load  per  panel  on  the 
chord  is  4,000  Ibs.  or  2  tons  and  Q  is  8.  In  Table  V, 
Chapter  VI,  it  is  seen  that  Q  for  two  angles  6"x4"xf£", 
with  the  long  legs  vertical,  is  2x17.7=35.4.  In  Table 
VI,  Chapter  IV,  it  is  seen  that  this  same  section  4  ft.  long 
has  a  strength  in  compression  of  98,000  Ibs.  75,000  di- 
vided by  98,000=r.77,  and  8  divided  by  35.4— .23.  The  sum 

118 


of  these  two  ratios  is  just  unity;  hence  this  section  is 
correct. 

(2)  Given  a  top  chord  supporting  a  reinforced  con- 
crete slab.  Panel  length,  12  ft.;  compression,  80,000  Ibs.; 
load  per  ft,  1,600  Ibs.  The  total  load  on  a  panel  is!2X 
1,600  Ibs.  or  9.6  tons,  and  Q  is  115.2.  By  Table  II,  Chap- 
ter VI,  Q  for  2-12"  channels  20.5  Ibs,  is  228.1.  By  Table 
XVI,  Chapter  IV,  the  same  channels  in  compression  for 
a  length  of  12  ft.  will  carry  161,000  Ibs.  The  sum  of  the 
two  ratios  will  be  found  to  be  close  to  unity.  It  is  to  be 
noted  that  this  channel  section  would  not  be  good  for 
161,000  Ibs.  if  it  were  not  supported  continuously  or  at 
close  intervals  laterally,  or  unless  the  channels  were  sepa- 
rated and  latticed,  as  indicated  in  Table  XVI,  Chapter  IV. 

A  common  method  of  providing  for  bending  in  the  top 
chord  of  a  roof  truss  is  by  using  a  web  plate  between  two 
angles,  such  sections  as  shown  in  Godfrey's  Tables,  page 
122.  By  using  the  section  modulus  as  found  in  that  table 
the  stress  in  such  member  due  <to  bending  may  be  found. 
An  approximate  method  is  as  follows: 

Find  the  size  of  a  pair  of  angles  that  will  take  the  com- 
pression, acting  alone;  then  fiind  the  size  of  a  web  plate 
which  at  16,000  Ibs.  per  sq.  in.  will  take  the  bending. 

The  following  table  will  facilitate  the  selection  of  a 
web  plate  to  take  the  bending  stress. 

TABLE  II. 

Capacity  of  Steel  Plates  in  Bending 

Fiber  Stress  16,000  Ibs.  per  sq  in. 
Q  is  product  of  span  in  ft.  and  unif.  load  in  tons. 


Size 

Size 

Size 

of 

Q 

of 

Q 

of 

Q 

Plate. 

Plate. 

Plate. 

6xJ4 

8.0 

11x3/6 

40.3 

16xM 

85.3 

6x& 

10.0 

HxH 

53.8 

16xJ^ 

113.8 

7x^ 

10.9 

12x3^ 

48.0 

17xH 

96.3 

7xA 

13.6 

12x^ 

64.0 

17x1^ 

128.5 

B*y4 

14.2 

13x3^ 

56.3 

18x3/6 

108.0 

8x& 

17.8 

13xH 

75.1 

18x^ 

144.0 

9x*4 

18.0 

14x3^ 

65.3 

19x/s 

140.4 

9x3/6 

27.0 

14xJ/£ 

87.1 

19x& 

180.5 

10x3/6 

33.3 

15x3/6 

75.0 

20x-&      |      155.5 

10x^ 

44.4 

15x^ 

100.0 

20xyV 

I    200.0 

Examples : 

(1)  Required  the  section  of  the  top  chord  of  a  roof 
truss ;  panel  length,  6  ft. ;  load  per  ft,  800  Ibs. ;  compres- 
sion, 28,000  Ibs.     By  Table  VI,  Chapter  IV,  it  is  seen  that 
2  angles  3"x2^"x54"  will  take  the   stress  of  28,000  Ibs. 
in  a  length  pf  6  ft.    The  load  on  the  chord  section  is  800X 
6r=4,800  Ibs.  or  2.4  tons.    Q  is  2.4X6=:14.4.    By  Table  II, 
this  chapter,  it  is  seen  that  an  8"x^4"  plate  will  take  the 
bending. 

(2)  Required  the  section  of  the  top  chord  of  a  roof 
truss,  the  length  of  panel  being  12  ft.  along  the  slope  and 
10   ft.   horizontally.     Load   per    ft.   along  the    slope,   2,000 
Ibs.;  compression  68,000  Ibs.     By  Table  VI,  Chapter  IV, 
it  is  seen  that  2  angles  6"x3^"x^"   will  take  the  com- 
pression.   The  load  on  the  chord  section  is  12X2,000=24,- 
000  Ibs.  or  12  tons.     Q  is  12x10=120.     (Since  10  is  the 
span  and  not  12.)     An  18"x7-16"  plate  has  a  value  Qz^ 
126. 


120 


CHAPTER  IX. 
Floor  Arches  and  Slabs. 

Table  I,  from  "Cambria  Steel"  gives  the  weight  and  safe 
load  per  square  foot  for  hollow  tile  floor  arches. 

TABLE  I. 

SAFE  LOAD  IN  LBS.  PER  SQ.  FT.  ON  HOLLOW  TILE  FLOOR  ARCHES 
(INCLUDING  WT.  OF  TILE  AND  ELOOR.) 

Depth  in  Wt.of  Arch  Span  of  Arch  in  Feet. 

In.        per  Sq.  Ft.        3  4  5  67  8 

Lbs. 


6 

27 

336 

189 

121 

7 

29 

429 

242 

155 

m 

8 

32 

523 

294 

188 

131 

9 

36 

616 

347 

222 

154 

113 

.  . 

10 

39 

709 

399 

255 

177 

130 

100 

12 

44 

896 

504 

323 

224 

165 

126 

In  order  to  realize  this  safe  load  the  beams  must  have 
tie  rods,  so  that  the  thrust  of  the  arch  will  not  come 
against  the  unstiffened  beam.  Tie  rods  in  hollow  "tile  con- 
struction are  very  often  inadequate,  as  a  little  calculation 
will  show.  Take  for  example  a  10-inch  arch  on  a  6-ft. 
span.  Assuming  a  total  load  of  150  Ibs.  per  sq.  ft.  and 
an  effective  depth  of  the  arch  of  6  inches,  the  thrust  per 
foot  of  the  arch  is  found  to  be  1350  Ibs.  It  is  common  to 
see  34-in.  tie  rods  spaced  6  or  8  ft.  apart  in  beams  of  this 
size.  At  6  ft.  the  stress  on  a  rod  is  8,100  Ibs.  or  about 
33,000  Ibs.  per  sq.  in.  on  the  rod  at  root  of  threads.  Be- 
sides this  heavy  stress  on  the  rod  the  side  force  on  the 
flange  of  the  beam  is  too  great,  and  rods  should  be  closer 
to  stiffen  the  flange.  In  addition  to  this  the  rods  are  very 
often  placed  at  the  middle  of  the  web  of  the  beam,  where- 
as they  should  be  near  the  bottom  flange,  say  about  3 
inches  from  the  bottom  of  the  beam. 

121 


It  is  true  that  the  thrust  of  one  arch  will  balance  that 
of  the  next  one,  but  this  does  not  apply  to  the  last  arch 
of  a  row,  where  a  single  tie  rod  is  often  made  to  take  the 
full  thrust  of  the  floor  arch. 


Fig.  I. 


A  good  practice,  and  one  that  ought  to  be  generally 
adopted,  is  to  double  the  number  of  tie  rods  for  all  outer 
arches  (as  shown  in  Fig.  1)  whether  these  are  adjacent 
to  a  stair  well  or  other  opening  in  the  floor  or  against  a 
wall.  The  side  of  a  brick  wall  is  not  a  suitable  abutment 
for  a  floor  arch ;  furthermore,  the  outside  channel  or  beam 
is  not  always  in  contact  with  the  wall.  By  this  method  the 
rods  in  interior  arches  may  be  6  or  8  ft.  apart,  while  "those 
in  outer  arches  will  be  3  or  4  ft.  apart. 

Tie  rods  are  usually  5/s",  3A",  and  7/%"  rods.  They  arc 
ordered  about  three  inches  longer  than  the  distance  center 
to  center  of  beams. 

Tile  arches  are  not  suitable  for  wide  spans  between  the 
beams.  The  upper  limit  should  be  about  7  or  8  feet.  In 
wide  spans  the  compression  in  the  tiles  becomes  great,  and 
the  manner  in  which  these  tiles  are  laid  does  not  inspire 
confidence  as  to  their  ability  to  resist  heavy  compressive 
stresses.  What  are  called  end  construction  tiles,  the  most 
common  in  use,  have  their  thin  webs  butting  together  and 
fitting  very  imperfectly.  The  filling  of  the  joints  with 
mortar  is  still  more  imperfect. 


122 


REINFORCED   CONCRETE    SLABS. 

Reinforced  concrete  floor  slabs  are  commonly  made  in 
thicknesses  of  about  3  to  7  or  8  inches.  The  principles  of 
reinforced  concrete  design  laid  down  in  Chapter  VI  apply 
also  to  slab  construction.  On  account  of  the  large  pre- 
dominance of  concrete  over  steel  and  the  resultant  stiff- 
ness of  the  slab  and  on  account  of  the  fact  that  tension 
in  this  concrete  is  ignored,  it  is  safe  to  use  16,000  Ibs.  per 
sq.  in.  as  the  calculated  working  stress  in  the  steel.  The 
safe  compressive  stress  of  600  Ibs.  per  sq.  in.  will  be  used 
in  the  concrete.  This  would  give  a  steel  area  of  .94  per 
cent,  of  the  area  of  the  slab,  when  the  balance  between 
steel  and  concrete  is  effected. 

The  span  of  a  slab  is  to  be  taken  as  the  clear  distance 
between  beams  or  other  supports,  and  the  slab  is  taken  as 
a  simple  beam  for  this  span.  No  allowance  for  supposed 
continuity  of  slabs  is  made. 

The  bending  moment  on  a  -slab,  by  the  above  standard  is 
as  follows: 

M=106  D2 

where  M  is  the  bending  moment  in  ft.-lbs.  per  ft.  width  of 
slab  and  D  is  the  depth  of  the  slab  in  inches. 

Table  II  is  worked  out  on  the  basis  of  the  above  formula. 
The  steel  reinforcement  is  given  in  square  rods.  Round 
rods  or  a  steel  mesh  having  the  same  sectional  area  per 
foot  width  of  slab  could  be  used.  The  steel  reinforce- 
ment should  lie  about  one-eighth  of  the  depth  of  slab 
from  the  bottom. 

PIAMCTCI** 


u 

^  SO  PlArw 

Fiq.Z.               U 

lETt«»                            -' 

~r^     _,       „      .£-   -- 

I 

ns.3. 

I 

123 


Generally  every  alternate  bar  or  every  third  bar  should 
be  bent  up  and  run  beyond  the  support,  as  indicated  in 
Figs.  2  and  3.  This  is  to  prevent  cracking  in  the  upper 
part  of  the  slab  at  the  supports.  Of  course  when  two 
slabs  come  together  on  a  beam,  these  extended  rods  will 
overlap.  This  is  not  shown  in  Figs.  2  and  3  because  of 
the  confusion  that  it  would  entail  in  these  sketches. 

Besides  the  main  reinforcement  in  a  slab  there  should 
be  transverse  reinforcement.  This  may  be  made  up  of 
%-in.  to  ^2-'m.  square  or  round  rods.  In  heavy  slabs  -/£-in. 
rods  may  be  spaced  2  ft.  apart.  In  light  slabs  /4-in.  rods 
may  be  spaced  one  ft.  apart.  These  rods  are  to  prevent 
shrinkage  cracks  in  the  slabs. 

For  maximum  economy  in  weight,  as  in  a  high  building, 
the  slabs  and  spans  should  be  about  in  the  relation  of 
those  in  Table  II.  There  are  many  circumstances  in  which 
it  is  economical  to  use  a  deeper  slab  than  those  shown  in 
the  table,  in  which  case  less  steel  reinforcement  can  be 
employed.  The  reason  for  this  is  that  a  large  part  of  the 


TABLE    II. 


Maximum  Span  in  Clear  between  Sup- 
ports for  Reinforced  Concrete  Slabs. 


Depth  of 

Slab  in 
Inches. 

Reinforcement 

: 

Maximum    Span   in    Feet   for   Total 
Uniform   Load   per    Sq.    Ft.    of 

Dia.  of 

Sq.  Rods 
in  In. 

Distance 
C.  to  C. 
of  Rods 
in  In. 

100|    125|    150 

ijDS.  |  U)S.  |  Us. 

175|   200 
Lbs.|Us. 

250|    300 
I,bs.|Lbs. 

2JA 

3H 

4 

4^ 
5 
5^ 
6 
6^ 

7H 

1A 

y* 

H 
H 
X 

i/2 

4 

3/4. 

2.7 
2.2 
4.3 
3.7 
5.9 
5.3 
7.6 
6.9 
6.4 
8.5 
8.  JO 
7.5 

7.3|    6.5|    5.9 
8.7J   7.8    7.1 
10.  2|   9.1|   8.3 
11.6|10.4|   9.5 
13.1111.  7)10.  7 
14.6  13.0  11.9 
16.  0114.  3113.1 
15.6114.3 
16.9|15.5 
18.2  16.6 
|  J17.8 

5.5|    5.1 
6.6     6.2 
7.7     7.2 
8.8|   8.2 
9.9|   9.3 
11.0J10.3 
12.1111.3 
13.2|12.4 
14.3)13.4 
15.4|14.4 
16.5115.4 
17.6116.5 

5.5 
6.4 
7.4 
8.3 
9.2 
10.1 
11.1 
12.0 
12.9 
13.8 
14.7 

5.9 
6.7 
7.6 
8.4 
9.2 
10.1 
10.9 
11.8 
12.6 
113.5 

(19.0 

124 


cost  of  a  reinforced  concrete  slab  is  in  the  forms.  An 
inch  or  so  more  of  concrete  does  not  make  much  differ- 
ence in  the  cost,  and  it  may  effect  considerable  saving  in 
the  steel. 

It  is  plain  'that  if  a  deeper  slab  than  that  shown  in  the 
table  is  used,  the  stress  in  the  concrete  will  be  less  as  also 
that  in  the  steel.  The  concrete  of  course  cannot  be  varied, 
but  the  steel  reinforcement  may  be  reduced.  The  stress  in 
the  steel  reinforcement  will  be  directly  proportional  to  the 
total  load  per  sq.  ft.  for  a  given  span  and  depth  of  slab. 
The  table  may  then  be  used  to  find  the  amount  of  'Steel 
needed  for  a  given  span  and  depth  and  a  load  different 
from  that  in  the  table,  as  follows : 

Given  a  span  8.2  ft.  in  the  clear  and  a  .slab  4  in.  deep, 
to  support  a  total  load  of  150  Ibs.  per  sq.  ft.  By  Table  II 
it  is  seen  that  this  slab  would  carry  200  Ibs.  per  sq.  ft. 
with  the  reinforcement  shown  in  the  table.  For  a  load 
of  150  Ibs.  per  sq.  ft.  the  reinforcement  would  need  but 
-)4  of  the  standard  area,  or  the  rods  may  be  spaced  4/3 
as  far  apart.  Four-thirds  of  3.7  inches  is  4.93  in.,  or  say 
5  inches.  Square  rods  ^  in.  in  diameter  and  spaced  5  in. 
would  then  be  used. 

Designers  and  constructors,  particularly  the  latter,  in 
dealing  with  reinforced  concrete  slabs  make  many  grave 
errors  in  the  matter  of  framing  around  openings  in  the 
floor.  It  is  common  but  very  bad  practice,  where  open- 
ings as  to  be  left  in  a  floor  slab,  to  cut  off  the  reinforcing 
rods  at  the  edge  of  the  opening  and  to  use  so-called  head- 
ers, 'that  is,  rods  parallel  to  the  side  of  the  opening.  This 
is  an  idea  borrowed  from  the  practice  in  wooden  joist 
framing,  but  the  user  of  this  idea  ignores  the  fact  that 
in  wooden  joist  framing  the  header  is  carried  by  double 
joists. 

Fig.  4  shows  the  common  but  erroneous  methods  of 
taking  care  of  openings  in  a  floor  slab.  The  rods  are  all 
laid  nicely  in  parallel  lines,  and  they  look  well  to  anyone 
ignorant  of  'their  office.  The  arrangement  shown  in  Fig. 
5  is  not  nearly  so  neat,  but  the  main  rods  reach  to  sub- 

125 


Fig.4- 


Pig.5 


stantial  bearings  in  every  case;  they  do  not  throw  their 
load  on  some  other  rod  already  burdened  with  its  full 
share. 

The  sides  of  the  rectangles  in  Figs.  4  and  5  represent 
walls  or  beams  supporting  a  slab.  The  cross  rods  in  Fig. 
5  are  not  "headers,"  but  are  merely  for  the  purpose  of  re- 
inforcing locally  the  slab  in  the  triangular  space.  Ex- 
panded metal  or  other  steel  mesh  could  be  used  in  these 
triangular  spaces. 

Another  error  in  laying  floor  rods  around  openings  is  to 
place  the  rods  parallel  up  to  the  opening  and  then  to  bend 
or  curve  them  in  plan  around  the  opening.  This  is  as  bad 
as  the  arrangement  of  Fig.  4.  Reinforcing  rods  should 
not  be  bent  or  curved  horizontally.  Rods  should  run 
straight  from  support  to  support.  If  the  opening  is  largo, 
special  beam  framing  should  be  made  around  it. 

In  tile-filled  ribbed  floors,  if  a  rib  must  be  omitted  on 
account  of  an  opening,  the  adjacent  ribs  should  make  up 
in  extra  thickness  and  reinforcement. 


126 


CHAPTER  X. 

* 

Structural  Details. 

No  attempt  will  be  made  in  this  book  to  cover  all  kinds 
of  structural  details,  for  the  reason  that  the  book  is  not 
one  that  aims  to  cover  structural  designing  in  all  its 
branches,  only  simple  riveted  structural  work  being  con- 
sidered. Details  of  pin  connected  members  will  be  omit- 
ted entirely.  As  stated  in  the  introduction,  the  book  is 
intended  to  cover  only  simply  design  as  applied  to  struc- 
tural parts  of  a  building. 

Rivets.  The  strength  of  a  rivet  has  two  phases,  as  ex- 
hibited in  the  two  ways  in  which  it  may  fail.  First  the 
rivet  may  fail  in  shear,  or  by  cutting  the  shank  in  the 
plane  of  the  surfaces  of  the  metal  joined.  Next  it  may 
fail  in  bearing,  or  by  crushing  against  the  metal.  When  a 
rivet  fails  in  shear,  it  is  cut  in  two  by  excessive  strain, 
such  as  would  result  from  the  action  of  shear  knives. 
When  it  fails  in  bearing,  the  metal  of  the  rivet  crushes 
against  the  side  of  the  hole,  allowing  the  parts  that  are 
joined  by  the  rivet  to  slip. 

The  strength  of  a  rivet  in  shear  is  measured  by  the 
area  of  steel  that  it  is  necessary  to  cut  in  the  shearing 
off  of  the  rivet,  that  is,  by  the  area  of  the  cross  section  of 
the  rivet  shank.  This  is  always  taken  as  the  area  of  the 
cross  section  of  the  rivet  before  driving. 

The  strength  of  a  rivet  in  bearing  is  measured  by  the 
projection  of  the  semi-intrados  of  the  rivet  hole  in  the 
plate,  that  is,  the  product  of  the  diameter  of  the  rivet 
and  the  thickness  of  the  plate.  Here,  too,  the  nominal 
diameter  of  the  rivet,  and  not  the  diameter  of  the  hole, 
is  used. 

The  unit  stresses  that  may  be  allowed  in  rivets  vary 
with  the  kind  of  work,  those  for  railroad  bridges  being 
low  and  those  for  quiescent  loads,  such  as  buildings,  be- 

127 


ing  higher.  Units  of  10,000  Ibs.  per  sq.  in.  for  shear 
and  20,000  Ibs.  per  sq.  in.  for  bearing  are  very  often  used. 
Better  units  are  9,000  and  18,000  respectively  Table  I 
gives  the  safe  value  of  rivets  on  the  basis  of  these  two 
sets  of  units  for  the  sizes  of  rivets  generally  used  in 
building  work. 


TABLE  I. 

Shearing  and  Bearing  Valve  of  Rivets. 
All  Dimensions  in  Inches. 


Diam. 

of 
Rivet. 


g 
Sh 


le. 

r. 
at 

9000 
Lbs. 


Bearing  Value  for   Different  Thickness  of  Plate   at   18,000 
Pounds  per  Square  Inch. 


tf  I  •&  1  K  I  *•  I    #  I    &  I    HI    Hi    Ml    II  I    u 


\  2760|2810i352014220;4920i  5630[  6330 


7030|  .....  |  .....  | 


8440|  9280|10130| 


Yl     |   3980|3380|422Q!5060[5910|   6750|   7590 

H      |   5410[3940|4920|  5910! 6890 1    7880|   8860*"9840Tl0830!  1 1 81 0|  12800  |'l 378 

1        I   7070 1 4500 1 5630  jeTsTT  |7880 1    9000 1 101301 11250f 123801 135001 14620| 1575 


Shin   |    Bearing  Value   for  Different  Thicknesses  of  Plate   at  20,000 

at     |  Pounds  per   Square   Inch. 

100001' 


Diam. 

of 
Rivet.     Lbs.  'I   y4   |   ft   |   H   I   &  I     1A   I     &   I     HI     HI     Ml     \\ 


|  3070|3130|3910|4690|5470i  6250|  7030|  7810) | | |.... 

|  4420|3750r4690|563G|6560|  750Q|  844G|  9380110310|11250[ ].... 

|  60101438015470 16570! 7660|  8750|  9840|10940|12030i  131301 14220|1531( 
|  7850 1 5000|6250j7500l  8750!  lOOOOJ  11250|  12500 113750 1 15000|  16250|  1750 


Bolts.  If  bolts  are  used  in  punched  holes,  take  two- 
thirds  of  the  values  in  the  table.  If  turned  bolts  in 
tight-fitting  reamed  or  drilled  holes,  the  bolts  having  J4-in. 
washers,  so  that  no  part  of  the  thread  is  in  the  hole,  the 
values  of  the  table  may  be  used. 

The  strength  of  the  connection  shown  in  Fig.  1  is  the 
single  shear  value  of  two  rivets,  for  evidently  these  two 
rivets  must  shear  before  the  connection  can  fail.  But  the 
strength  of  the  connection  is  also  that  of  the  two  rivets 
in  bearing  either  against  the  plate  or  the  angle,  for  if  this 

128 


metal  is  too  thin,  it  will  be  crushed  by  the  pressure  of 
the  rivet.  By  reference  to  Table  I  it  can  be  readily  seen 
which  is  less,  bearing  or  shear,  and  hence  which  is  the 
real  gage  of  the  strength  of  the  joint.  Suppose,  for  exam- 
ple that  the  metal  of  the  angle  is  J4  m-  thick  and  the 
rivets  are  34  m-  in  diameter.  ,  The  value  of  a  rivet  in 
single  shear  is  3,980,  and  in  bearing  3,380.  The  latter 
value  governs.  If  the  rivets  were  ^  m->  single  shear 
would  govern,  at  2,760.  Note  that  the  values  in  the  table 
between  the  heavy  zig-zag  lines  are  greater  than  single 
shear  and  less  than  double  shear. 


I  o    o  i 


Fig.  I. 

The  strength  of  the  connection  shown  in  Fig.  2  is  the 
double  shear  value  of  two  rivets,  or  four  times  the  single 
shear  value  of  one  rivet,  for  to  fail  in  shear  eaoh  of 
these  rivets  must  be  sheared  twice.  The  strength  of  the 
connection  is  also  that  of  two  rivets  in  bearing  against 
the  plate  or  the  double  thickness  of  angles.  If,  for  exam- 
ple, a  5^-in.  plate  be  used  and  ^-in.  angles,  -the  thick- 
ness of  plate  will  govern  so  far  as  bearing  is  concerned, 
and  in  %-in.  rivets  the  strength  is  9,840X2  or  19,680  Ibs. 
Double  shear  on  two  rivets  is  good  for  5,410X4,  or  21,640 
Ibs.  The  former  value  governs.  If  the  plate  were  11/16 
in.  or  more  in  thickness,  shear  would  govern.  In  ^4 -in. 
rivets  shear  would  govern  with  the  5^-in.  plate.  This  is 
indicated  by  the  zig-zag  line  of  Table  I. 

The  foregoing  rules  and  principles  apply  for  rinding  the 
strength  of  the  end  connections  of  tension  or  compression 
members,  or  the  strength  of  tension  splices,  or  the 
strength  of  the  end  connection  of  beams  and  girders. 


129 


The  rivets  in  any  riveted  connection  should  be  sym- 
metrically disposed  about  the  line  of  application  of  the 
stress,  insofar  as  it  is  practicable  to  effect  this  condition. 
This  is  to  avoid  eccentric  stress  on  the  rivets.  If  it  is 
necessary  to  place  rivets  unsymmetrical  with  respect  to 
the  line  of  stress,  additional  rivets  must  be  used. 

No  rivet  connection  should  be  made  with  less  than 
two  rivets,  preferably  not  less  than  three. 


Fig.  3. 


Frequently,  in  order  to  cut  down  the  size  of  the  gusset 
plate,  lug  angles  are  used  to  take  some  of  the  rivets  in 
the  end  connection  of  a  member  as  shown  on  the  diagonal 
members  of  Fig.  3.  Generally  the  larger  number  of  rivets 
should  be  in  the  member  itself. 

Tension  Splices.  Splices  in  tension  members  should  be 
made  with  splicing  pieces  having  a  net  sectional  area 
through  any  cross  section  (whether  at  right  angles,  dia- 
gonally, or  zig-zag  across  the  section)  equal  to  the  net 
sectional  area  of  the  piece  cut.  There  must  be  rivets 
enough  on  each  side  of  the  cut  to  take  the  full  stress 
in  the  member  spliced. 

Compression  Splices.  Splices  in  compression  members 
are  generally  made  by  planing  the  ends  of  the  members 
square,  so  that  they  will  fit  exactly  one  on  the  other  and 
providing  a  sufficient  number  of  splice  plates  to  hold  these 
planed  ends  rigidly  in  line. 

In  building  columns  made  of  I-shaped  sections  there 
should  be  a  plate  on  the  outside  of  each  flange  with  about 


130 


six  rivets  above  and  below  the  cut  in  each  plate.  There 
should  also  be  a  plate  on  each  side  of  the  web  of  the 
column. 

In  columns  made  of  two  channels  and  two  plates  it  is 
preferable  to  use  a  horizontal  plate  besides  the  splices  on 
the  cover  plates.  The  reason  for  this  is  that  the  webs  of 
the  channels  may  not  be  opposite  one  another,  and  splicing 
plates  on  these  webs  cannot  be  riveted,  as  the  section  is  a 
closed  one. 

Wherever  there  is  a  change  in  the  general  size  of  a  col- 
umn there  should  be  horizontal  plates  used  in  the  splice, 
so  as  to  distribute  the  load  of  the  upper  column  into  the 
lower. 

When  only  a  portion  of  a  compression  member  is  cut 
and  spliced,  the  full  area  and  the  full  number  of  rivets 
should  be  used  in  the  splice,  even  though  the  spliced  part 
has  the  ends  milled  for  a  bearing ;  for  in  building  up  such 
piece  in  the  shop  the  milled  ends  may  not  be  in  contact. 
It  is  practically  impossible  to  insure  close  contact. 

End  Connections  of  Beams.  The  end  connections  of 
beams  are  commonly  made  according  to  the  standards 
found  in  the  Carnegie  Pocket  Companion  (or  Godfrey's 
Tables,  pages  37  and  38). 

Channels  should  have  the  same  symmetrical  end  con- 
nection as  beams  of  the  same  depth.  Where  this  is  not 
practicable,  a  6"X6"  angle  may  be  used  with  two  rows  of 
rivets  in  each  leg. 

Beams  connecting  to  columns  are  usually  supported  on 
a  shelf  angle  riveted  to  the  column  and  are  riveted 
through  the  flange  to  the  same.  An  upper  angle,  shipped 
loose  with  the  column,  is  riveted  in  the  field  to  the  top 
flange  of  the  beam  and  to  the  column. 

When  more  than  four  rivets  are  required  to  carry  a 
beam  or  a  girder  on  a  shelf,  stiffener  angles  are  used  to 
take  the  additional  rivets.  These  should  be  placed  with 
the  outstanding  legs  directly  under  the  beam. 

131 


End  Connections  of  Girders.  When  a  girder  rests  on 
a  support  such  as  the  top  of  a  column  or  a  shelf  having 
stiffeners  under  it,  the  metal  of  the  column  or  of  stiffener 
angles  or  diaphragms  in  the  head  of  the  column  or  the 
stiffener  angles  below  the  shelf  should  be  directly  oppo- 
site the  metal  of  the  end  stiffeners  of  the  girder.  This 
is  an  important  feature  of  design  that  is  very  often  over- 
looked. It  is  illustrated  in  Fig.  4.  If  the  end  angles  of 
this  girder  were  turned  with  the  outstanding  legs  at  the 
end  of  girder,  these  angles  would  not  be  opposite  the 
metal  of  the  channel  of  the  column.  The  result  would 
be  excessive  bending  either  in  the  top  plate  of  the  colmun 
or  in  the  flange  angles  of  the  girder. 


g 

0 

o    o 

°0 

o 

0 
0 
0 

o 

1 

o         \ 

0 

o 

0 

o     o 

I 

I 

Pin 

4. 

r 

in  5 

J 

IJJ.3 

When  the  end  connection  of  a  girder  is  with  angles 
connecting  to  the  web  of  the  girder,  there  must  be 
enough  rivets  through  the  web  of  the  girder  to  take  the 
full  end  reaction  of  the  girder.  These  rivets  are  in  bear- 
ing on  the  web  of  the  girder,  even  though  some  of  them 
pass  through  the  flanges  of  the  angles  also.  If  there  is  not 
room  enough  for  the  required  number  of  rivets,  on  the 
basis  of  this  bearing  value  in  the  web,  the  fillers  can  be 
extended  as  in  Fig.  5.  The  four  additional  rivets  shown 
in  this  figure  unite  these  fillers  and  the  web  plate  so  as 
to  increase  the  value  of  the  five  rivets  in  the  angles. 

The  field  rivets  in  the  girder  connection  of  Fig.  5  will 
have  a  strength  of  14  rivets  in  single  shear  or  in  bear- 
ing either  on  the  angles  or  the  metal  to  which  they  con- 

il£Ct. 

132 


Seven-eighth-inch  rivets  are  used  in  flanges  as  nar- 
row as  3  inches;,  $4-in.  rivets,  in  flanges  as  narrow  as  2% 
inches;  ^-in.  rivets,  in  flanges  as  narrow  as  2  inches. 
When  it  is  known  that  %-in.  rivets  are  to  be  used,  the 
design  must  be  made  with  this  fact  in  view  and  flanges 
less  than  2^  in.  wide  must  not  be  placed  where  rivets 
will  have  to  be  driven  in  them.  The  same  must  be  ob- 
served with  other  sizes.  It  is  preferable,  because  of  econ- 
omy in  the  shop,  to  use  only  one  size  of  rivet  in  a  piece 
of  work.  An  exception  may  be  made  in  the  case  of  chan- 
nel flanges,  as  these  must  often  take  smaller  rivets  than 
the  rest  of  the  work.  They  must  be  handled  twice  in  any 
event  to  punch  web  and  flange  holes,  as  these  require  sepa- 
rate dies. 

Rivets  should  be  spaced  not  less  than  three  diameters 
apart  center  to  center,  nor  generally  more  than  six  inches 
apart.  They  should  not  be  closer  to  the  edge  of  metal 
than  about  two  diameters  (two  times  the  diameter  of  the 
rivet). 

Lattice  bars  for  single  lacing  should  be  about  60  de- 
grees with  the  axis  of  the  member.  Lattice  bars  for  dou- 
ble lacing  should  be  about  45  degrees  with  the  axis  of  the 
member.  Some  common  sizes  of  lattice  bars,  with  the 
depth  of  member  in  which  they  may  be  used  are  given 
in  the  following-  list : 


Size  of  bar. 

Depth  of  member. 

Size  of   rivets. 

iy2X  y4 
mx  y4 

2    x5/16 
2^x  & 
2^x7/16 

6   in.   and   under 
7   to  8  in. 
9  to  12  in. 
13  to  16  in. 
17    in.    and    upward 

5/s 

5/8 

tt 

H 

tt  or  % 

In  general  rivets  should  not  be  used  in  tension,  that  is, 
in  stress  that  tends  to  pull  the  heads  off.  If  it  is  neces- 
sary to  use  rivets  in  tension  no  less  than  four  should  be 
used  in  the  joint,  and  these  must  be  symmetrical  with  the 
application  of  the  load.  The  angles  used  should  be  of 
thick  metal,  so  that  they  will  not  bend  under  the  load,  pre- 
ferably V%  in.  or  ^  in.  thick. 

133 


For  tension  on  rivet  heads  use  no  more  than  one  half 
of  the  single  shear  value. 

Separators  are  made  either  of  short  pieces  of  gas  pipe 
or  of  castings.  (See  Godfrey's  Tables,  page  33.)  These 
are  the  pieces  that  are  placed  between  double  beams  to 
hold  them  a  given  distance  apart  and  to  take  the  bolts  that 
united  the  beams.  Usually  separators  in  double  beam 
work  are  placed  about  4  or  5  feet  apart.  The  office  of 
separators  in  some  cases  is  to  distribute  load  that  may 
be  applied  to  one  beam  only  of  a  pair,  so  that  they  will 
deflect  together.  In  cases  where  afll  or  nearly  all  of  the 
load  is  delivered  to  one  beam  of  a  pair,  as  when  floor- 
beams  connect  to  the  web  of  one  beam  of  the  pair,  ordi- 
nary cast  separators  are  not  sufficient.  In  such  cases 
there  should  be  riveted  diaphragms  between  the  beams. 
These  may  be  opposite  the  beam  connections. 

Beams  resting  on  walls  should  have  anchors  at  the 
ends.  The  usual  anchor  is  a  plain  24-in.  round  rod  6  in. 
long  .for  beams  up  to  10  in.  and  12  in.  long  for  larger 
beams.  A  hole  is  punched  in  the  web  of  the  beam  2  in 
to  4  in.  from  the  end  to  receive  the  anchor.  The  anchor 
rod  is  usually  kinked  at  the  middle.  A  pair  of  6x4  angles 
2  or  3  in.  long,  riveted  to  the  web  of  the  beam,  may  also 
be  used  as  an  anchor. 

Details  in  Timber  Trusses.  The  details  in  timber  work 
are  very  often  neglected  or  given  little  consideration,  or 
they  may  be  left  to  the  workmen  to  work  out  on  the  job. 

The  strength  of  bolts  and  spikes  can  not  be  so  definitely 
determined  as  that  of  rivets  in  steel  work.  Some  stand- 
dard,  however,  should  be  used.  The  following  table  is 
recommended  for  ordinary  conditions  in  sound  wood  of 
•the  hardness  of  yellow  pine.  For  white  pine  deduct  20 
per  cent. 

134 


TABLE  II. 

VALUE    OF    BOLTS    OR    SPIKES    IN    SHEAR. 

Diameter  in  ins. — 

y8    3/16    Y4  5/16    3/8      y2      5/8      ti        7/s          1 
Load  in  Ibs. — 

40      80     150    200    300    500    800    1200    1600    2000 

Table.  II  is  based  primarily  on  the  value  of  a  spike  or 
bolt  in  bending,  for  in  the  ordinary  case  the  spike  will 
bend  in  the  wood  before  it  will  shear  off.  In  using  the 
term  shear  in  the  heading  of  the  table  it  is  meant  to  con- 
vey the  idea  that  the  stress  on  the  bolt  or  spike  is  at  right 
angles  to  the  axis.  It  is  assumed  that  the  thickness  of  the 
wood  will  be  such  as  to  give  proper  bearing  against  the 
same,  as,  for  example,  not  less  than  one-inch  boards  for 
J.^-in.  bolts,  and  not  less  than  2-in.  boards  for  one-inch 
bolts.  If  the  pressure  is  tranverse  with  the  grain  of  the 
wood,  use  one-half  of  the  values  in  Table  I. 

The  distance  between  bolts  along  the  grain  and  from 
a  bolt  to  the  end  of  a  piece  should  not  be  less  than  about 
six  times  the  diameter  of  the  bolt. 


• 


Fig. 6.  Fi9-7 

Figs.  6  and  7  illustrate  two  kinds  of  splices  in  wood. 
For  full  efficiency  in  the  splice  of  Fig.  6  the  sum  of  the 
widths  of  the  two  splicing  pieces  (if  of  wood)  should  be 
equal  to  the  piece  spliced,  or  2h  should  equal  b.  However, 
the  full  tensile  strength  of  members  in  wood  is  not  often 
demanded.  In  a  4"x8"  piece  with  one-inch  bolts  the  net 
section  would  be  4\6=24  Sq.  m.  At  1,600  Ibs.  per  sq. 

135 


in.  this  would  take  a  tension  of  38,400  Ibs.  The  six  bolts 
in  double  shear  are  good  for  12X2,000=24,000  Ibs.  The 
distances  a  should  be  six  inches. 

The  splice  shown  in  Fig.  7  is  with  steel  or  cast  iron 
plates  having  gibs  at  the  ends.  Here  the  bolts  are  used  to 
hold  the  plates  together,  cy^e  measures  the  net  area  in 
tension.  2gXe  measures  the  area  in  bearing  against  the 
gibs,  which  has  a  value  of  800  and  1,000  Ibs.  per  sq.  in. 
for  white  pine  and  yellow  pine  respectively.  2/X?  mea- 
sures the  area  in  shear  along  the  grain.  Wood  is  par- 
ticularly weak  in  this  respect,  so  that  a  comparatively 
large  area  is  needed  here.  For  white  pine  use  80  Ibs.  per 
sq.  in.,  and  for  yellow  pine  use  100  Ibs.  per  sq.  in.  for 
this  shearing  value. 

One  of  the  most  important  and  difficult  details  to  take 
care  of  in  wood  is  this  one,  where  the  wood  is  in  longi- 
tudinal shear.  In  many  details  the  wood  is  notched,  as 
for  the  inclined  end  post  of  a  truss,  and  a  tension  is  ap- 
plied at  this  notch.  Frequently  the  distance  from  this 
notch  to  the  end  of  the  piece  is  not  sufficient  to  develop 
the  tension  of  the  piece  at  a  proper  safe  shear  on  the 
fibers  of  the  wood. 

Figs.  8  to  15  inclusive  show  various  methods  of  con- 
necting the  inclined  end  post  or  rafter  to  the  bottom 
chord  or  tie  in  a  wooden  truss. 

Trusses  are  often  built  up  of  two-inch  plank  as  indi- 
cated in  Fig.  8.  They  may  be  bolted  or  spiked  together. 
Filling  or  separating  blocks  should  be  used  at  interme- 
diate points  in  long  compression  members.  There  are  sev- 
eral advantages  in  this  kind  of  construction.  Pieces  can 
be  more  easily  handled,  details  can  be  more  readily  made, 
and  the  lighter  pieces  are  in  better  condition  for  season- 
ing. 

The  diagram  in  Fig.  11  indicates  the  method  of  finding 
the  tension  in  the  bolt.  The  side  ba  of  the  triangle  is  the 
stress  in  the  rafter.  On  the  same  scale  be  is  the  tension 
in. the  bolt. 

136 


Fig.  \  5 


137 


Fig.  1 9. 


•If — ^ 


Fig  ZO 


138 


Figs.  16  to  20  inclusive  show  other  details  in  wooden 
construction. 

Attention  is  called  to  the  caps  or  corbels  in  Fig.  20.  The 
one  marked  CD,  together  with  the  knee  braces,  could  be 
counted  upon  to  relieve  the  load  in  the  timber  beam  above 
the  post,  if  that  load  is  a  symmetrical  one;  but  AB  can- 
not offer  such  aid  except  by  putting  a  bending  moment  in 
the  post.  It  is  an  error  to  rely  upon  such  construction 
as  that  shown  to  the  left  of  Fig.  20  for  any  other  pur- 
pose than  to  brace  the  building. 


139 


CHAPTER  XI. 
Estimating  Loads. 

For  estimating  the  load  carried  by  a  beam  or  truss,  use 
the  following  data : 

Wood    4  Ibs.  per  sq.  ft.  one  inch  thick 

Stone    concrete     13     "       "        "          ' 

Cinder   concrete    9 ' 

Brick   walls    10 

Stone  walls  (not  granite)  13 

Granite     14 

Lime  mortar   9 

Hollow  brick  arches  weigh  about  8  Ibs.  per  sq.  ft.  per 
inch  of  thickness. 

Ordinary  tile  arches  weigh  about  4  Ibs.  per  sq.  ft. 
per  inch  of  thickness. 

Tile  partitions   weigh   as    follows: 

WEIGHT   PER    SQ.    FT. 

2-in.        3-in.       4-in.         5-in.       6-in. 

Semi-porous    . . . .   12  Ibs.     15  Ibs.     16  Ibs.     18  Ibs.    24  Ibs. 
Porous    14  Ibs.     17  Ibs.     18  Ibs.     20  Ibs.    26  Ibs. 

Book  tile  or  flat  tile  for  ceilings  and  roofs  are  made 
in  lengths  of  16,  18  and  20  inches  in  2-in.  tile;  16,  18,  20 
and  24  inches  in  3-in,  tile ;  and  24  inches  in  4-in.  tile.  The 
2-in.  tile  weigh  12  Ibs.  per  sq.  ft. ;  the  3-in.  tile,  20  Ibs.  per 
sq.  ft.;  the  4-in.  tile,  22  Ibs.  per  sq.  ft. 

For  wooden  shingles  on  a  roof  allow  2*4  Ibs.  per  sq. 
ft.,  for  slate  shingles  allow  5  to  7  Ibs.  per  sq.  ft.  For 
Spanish  tiles  allow  7>^  to  8  Ibs.  per  sq.  ft.  For  tarred 
felt  and  gravel  or  slag  allow  2  Ibs.  per  sq.  ft.  for  the  felt 
and  tar,  3  Ibs.  per  sq.  ft.  for  slag,  and  4  Ibs.  per  sq.  ft. 
for  gravel. 

For  slate  tiles  allow  14  Ibs.  per  sq.  ft.  per  inch  of  thick- 
ness. For  solid  clay  tiles  allow  11  Ibs.  per  sq.  ft.  per  inch 
of  thickness 

140 


For  corrugated  steel  in  gages  of  16,  18,  20  and  22,  allow 
3.6,  2.7,  1.9  and  1.5  Ibs.  per  sq.  ft.  respectively. 

In  ordinary  floor  work  the  steel  beams  will  weigh,  in 
pounds  per  sq  ft  of  floor,  about  one-third  of  the  span  in 
ft,  and  the  girders  one-fifth  of  their  span  in  feet  Thus, 
if  the  span  of  the  beams  is  15  ft.,  use  5  Ibs.  per  sq.  ft. 
for  a  trial  weight  or  the  beams;  if  the  span  of  the  girders 
is  20  ft.,  use  4  Ibs.  per  sq.  ft.  for  a  trial  weight  of  the 
girders. 

For  trusses  carrying  roof  loads  only  use  one-tenth  of 
the  span  for  a  trial  load  per  sq.  ft. 

For  steel  columns  estimate  the  weight  per  lineal  foot  at 
about  four  times  the  area  of  the  section  in  square  inches. 

Ordinary  partitions  in  a  building  are  usually  considered 
as  covered  in  the  allowance  for  live  load.  When  an  al- 
lowance is  made  for  their  weight,  it  may  be  in  a  uniform 
load  of  say  5  or  10  Ibs.  per  sq.  ft.  Fire  walls  around 
elevator  shafts  and  'the  like  are  taken  at  their  full  weight 
for  the  beam  on  which  they  are  built. 

For  exterior  walls,  estimate  the  weight  per  running  foot 
for  a  solid  wall  and  deduct  the  proportion  of  the  wall  oc- 
cupied by  windows  or  other  openings. 

The  New  York  Building  Code  allows  a  reduction  of 
the  live  load  on  columns  carrying  several  floors  as  fol- 
lows : 

For  top  story  use  full  live  load. 

For  next  story  use  full  live  load. 

For  each  succeeding  story  deduct  5  per  cent  from  full 
live  load  until  50  per  cent  of  live  load  is  reached.  Use 
50  per  cent  of  live  load  for  all  remaining  stories. 


141 


INDEX 


Allowed    pressure   on    soils, 

Allowed  stresses  in  rein- 
forced concrete  beams,  65. 

Allowed  stresses  on  wooden 
posts,  18. 

Allowed  stress  on  cast  iron 
posts,  21. 

Anchorage   of   rods,    63,    64. 

Anchors   for   beams,    134. 

Angles  in  bending,  capacity 
of—  59. 

Areas  of  squares  and  cir- 
cles, 21. 

Batten   plates   on   posts,   29, 

Beams,    49,    74. 

Beam  seats,   24. 

Bearing  plates,  88. 

Bearing  power  of  soils,  3. 

Bending  moments  on 
beams,  54. 

Bending  moments  on  gird- 
ers, 76,  77. 

Bethlehem    beams,    58,    59. 

Bethlehem   columns,    28. 

Bolts,    128. 

Bolts  and  spikes  in  wood, 
135 

Box  girders,  77,  78,  89,  90, 
91. 

Bracing  of  beams.   51,   52. 

Bracing  of  buildings,   1. 

C,    (coefficient),    49. 
Cantilevers,    54,    57,    91. 
Capacity   of  beams,   58-60. 
Capacity  of  box  girders,   78, 

90. 
Capacity     of    plate    girders, 

81,    82. 
Cast  iron  bases  for  columns, 

14,  15. 

Cast  iron  beams,  50. 
Cast    iron     column     details, 

24 

Cast  iron  columns,  20-24. 
Channel  columns,  27,  28,  42- 

Clay,  bearing  power  of — ,  3. 
Column  bases,  14,  15. 
Column    footings,    8,    11.    12, 

13. 

Column  formulas,   25. 
Column  loads,  16. 
Columns     and     other     com- 
"  pression   members,   16-46. 


Columns,  loading  of — .  17. 
Compression     members,     16- 

46,    116. 

Concrete  piles,    5. 
Concrete   steel    columns,    32, 

33 

Corbels,    139. 
Cover  plates,   77,   78,   79,    84, 

86. 

Depth   of  beams,    49,    52,   63. 
Details    of    timber    trusses, 

134-139. 
Diameter       of       reinforcing 

rods,     63. 

End   connections    of    beams, 

131. 
End   connections   of  girders, 

132. 

Estimating    loads,    140,    141. 
Eye-bars,    114. 

Factor   of   safety,    25. 
Flange  plates,  77,  78,  79,  84, 

86. 
Floor  arches  and  slabs,  121- 

126. 

Footings,    7-13. 
Foundations,  3-6. 

Gas    pipe    columns,    28,    29, 

37. 
Girder        beams,        capacity 

of—,    59. 
Girders,    75-92. 
Graphical       calculation       or 

stresses,    95-97. 
Grillages,  11. 

Hooks   in  rods,   63. 

I-beam  columns,   27. 
I-beams,    capacity    of — ,    58. 

Knee   braces,    139. 

lattice   bars,    133. 
Lattice  in  columns,  29. 
Lean-to   trusses,    94. 
Limits    of    column    lengths 

27. 

Lintels,    47,    48. 
Lintels,  cast  iron — ,   50. 
Loop  rods,   115. 


142 


Weedle  beams,   10. 
Net     section     of     members, 
113,   114. 

Openings  in  floors,  125,  126. 

Panel  loads,   95. 

Partitions,  weight  of — ,  16, 
141. 

Piles,  5. 

Plate  girders,    80-84. 

Pressure  on  footings,  calcu- 
lation of — ,  5. 


Q,    (coefficient),   61. 


Single  angles  in  tension, 
113. 

Splices,   131,   135,   136. 

Spreading   beams,    56. 

Star-shaped  columns,  27,  36. 

Steel  beams,  51-60. 

Steel    columns,    25-30. 

Steel  truss  members  in 
bending,  118,  119. 

Stiffeners  in  girders,  85,  87, 
132. 

Stirrups  in  reinforced  con- 
crete beams,  61,  62. 

Straight  line  formula,   26. 

Strength  of  columns,   25. 

Structural   details,    127-139. 


Batio  of  slenderness,  18,  26. 

Reinforced  channel  beams, 
77,  78. 

Reinforced  concrete  beams, 
61-74. 

Reinforced  concrete  beam 
tables.  69-74. 

Reinforced  concrete  col- 
umns, 30-32. 

Reinforced  concrete  slabs, 
123-126. 

Reinforced   I-beams,    77,    78. 

Rivets   in   tension,    133,    134. 

Rivets,    127-130,    133. 

Rivet  spacing  in  girders,  84, 
89. 

Rules  for  reinforced  con- 
crete beam  design,  62-64. 


Selecting  column  sections, 
30. 

Separators,    12,   134. 

Settlement  of  buildings,  4, 
6. 

Sharp  bends  in  rods,   61,   63. 

Shear  in  plate  girders,  83, 
84,  85. 

Shear   on   wood,   136. 

Shear  reinforcement  in  re- 
inforced concrete  beams, 
63,  65,  66. 

Sheet  piling,   4. 

Sign   of  stresses,    93,   96,   97. 

Single  angle  columns,  28, 
29,  34. 


Tee-bars  in  bending,  capac- 
ity of — ,  60. 

Tensile  strength  of  thread- 
ed rods,  114. 

Tie  rods,   121,  122. 

Tile  arches,  121,  122. 

Tension  members,  113,  114, 
115. 

Trusses,     93-120. 

Truss  members  in  bending, 
116. 

Unbraced    beams,    52. 


Wall  footings,  7,   10. 

Wall   plates,    88. 

Walls,   weight   of — ,    17. 

Webs   of  plate   girders,    85. 

Width  of  reinforced  con- 
crete beams,  64. 

Wooden  beams,    49,   50. 

Wooden    columns,    17-19. 

Wooden    piles,    5. 

Wooden  post  splice,  19. 

Wooden  truss  members  in 
bending,  117. 


Zee-bar  columns,  28. 
Zee-bars  in  bending,  capaO 
ity— ,  60. 


143 


WILSON  ROLLING  DOORS,  either  steel 
or  wood,  are  the  most  satisfactory  method  of  clos- 
ing openings.  They  afford  an  absolute  protection, 
are  easy  to  operate,  difficult  to  destroy,  and  last 
but  not  least,  they  cost  little  to  erect.  If  you  are 
interested  write  for  the  fine  catalogue  we  have 
prepared  on  the  subject  and  for  full  size  detail 
sheets.  Your  request  will  bring  them  postpaid. 


J.  G.  WILSON  MANUFACTURING  CO. 

Bancroft  Building,  NEW  YORK, 


148 


"TOCKOLITH" 

(Patented) 


A  CEMENT  PAINT  which  will  render  immune 
to  corrosion,  all  metals  to  which  it  is  applied. 

In  setting,  "Tockolith"  generates  Calcium  Hy- 
droxide (Lime)  in  minute  quantities,  and,  this 
material  being  the  best  inhibitive,  prevents  the 
metal  from  rusting. 

Tockolith  should  be  second-coated  with  one  of 
our  "R.  I.  W."  DAMP  RESISTING  PAINTS,  as 
a  guard  against  electrolysis. 

"DIFFERENT  FROM  ALL  OTHER  PAINTS." 

TOCH  BROTHERS 

Established  1848. 

-  Manufacturers  of  - 

TECHNICAL     PAINTS,     ENAMELS,      VARNISHES     AND 
DAMPPROOFING    COMPOUNDS. 

320  Fifth  Avenue, 
NEW  YORK,  N.  Y. 

WORKS:     Long  Island  City,  N.    Y.  and  Toronto,   Ont..   Can. 


Fireproof   In    Reality — Not   Only   In    Name. 


Xs!?  1 


ANCHOR 


ISO 


By  the  use  of  re-inforced  concrete  construction,  the  walls, 
floors  and  partitions  of  a  building  may  be  made  fireproof. 
By  the  use  of  "Dahlstrom"  Metal  Doors  and  Trim  the  fire- 
proofing  is  completed,  and  protection  is  provided  for  the 
contents  and  the  lives  of  the  occupants  of  such  a  building, 
making  it  "Absolutely"  fireproof  in  reality,  as  well  as  in 
name. 

The  illustrations  herewith  show  different  methods  of  prop- 
erly installing  "Dahlstrom"  Doors  and  Trim  in  reinforced 
concrete  partitions. 

In  Section  No.  1  is  shown  an  angle  iron  frame  connected 
by  perforated  anchor  plates.  The  frames  are  shop  made  to 
proper  size  for  the  doors  and  are  set  in  position  before  the 
concrete  is  poured.  The  concrete  passing  through  the  per- 
forations will  securely  anchor  the  frame  in  position  and 
affords  a  good  fastening  for  the  finished  Metal  Trim. 

Section  No.  2  shows  perforated  channel  shaped  clips  of 
sizes  to  suit  the  thickness  of  the  concrete.  These  are  laid 
in  the  forms  as  the  concrete  is  poured,  leaving  the  2"  flanges 
exposed  on  each  side  of  the  partition  after  the  forms  are 
taken  down.  A  I"xj4"  channel  is  'then  applied  by  machine 
screws  which  are  tapped  into  the  flanges  of  the  perforated 
clips.  These  channels  will  then  serve  as  grounds  for  the 
plaster,  and  also  to  fasten  the  finished  steel  jambs  to,  which 
are  made  adjustable  so  as  to  take  up  any  possible  variation 
in  the  thickness  of  the  partition. 

Another  method  of  construction  for  concrete  partition  is 
shown  in  section  No.  3.  In  this  case  the  bucks  are  of  re-in- 
forced concrete  made  up  separately  and  erected  before  the 
partitions  are  placed.  Provision  for  fastening  the  flanges  of 
the  steel  jambs  is  made  by  sleeves  or  holes  through  the 
bucks,  through  which  the  fastening  bolts  can  pass. 

Additional  information  and  submis- 
sion drawings  to  meet  special  re- 
quirements will  be  cheerfully  furn- 
ished by  applying  to 

Dahlstrom  Metallic  Door  Co. 

Executive  Offices  and  Factories, 
3  BLACXSTONE  AVENUE. 
JAMESTOWN,   N.   Y. 


Why  Every  Man  Who  Is  Interested  In  Con* 
crete  Design  or  Construction  Should 
have  a  Copy  of 

"CONCRETE" 

by  Edward  Godfrey 

BECAUSE — it  is  not  an  automatic  designer,  but  aims  to 
show  how  to  design  by  teaching  the  principles  of  design. 

BECAUSE — There  are  things  in  this  book  that  are  not 
found  in  any  other  book  in  any  language. 

BECAUSE — the  book  points  out  many  prevalent  errors  in 
current  and  permanent  literature  on  the  subject  of  con- 
crete construction.  Some  of  these  errors  are  the  work 
and  the  utterances  of  the  most  eminent  engineers  and 
authorities  enjoying  the  highest  reputation. 

BECAUSE — it  contains  444  pages  of  live  information  on 
this  live  subject. 

BECAUSE — it  tells  how  to  design  concrete  and  reinforced 
concrete  beams,  slabs,  columns,  chimneys,  arches,  domes, 
conical  roofs,  vaults,  retaining  walls,  dams,  foundations, 
etc.  It  tells  also  how  not  to  design  these. 

BECAUSE — it  contains  a  series  of  articles  that  appeared  in 
the  Engineering  News  in  1906,  which  brought  out  so  much 
discussion  that,  after  filling  36  columns  with  the  articles 
and  discussion,  the  editor  refused  to  print  any  more,  un- 
less something  very  important  and  new  should  be  brought 
out.  All  of  these  articles  and  the  discussion  are  reprinted 
in  the  book. 

BECAUSE — it  contains  a  series  of  articles  published  in 
1907  in  Concrete  Engineering,  which  also  brought  out  much 
discussion.  Three  of  these  articles  were  very  fully  quoted 
in  that  excellent  periodical,  The  Engineering  Digest. 

BECAUSE — it  contains  31  pages  of  drawings  showing 
standard  practice  in  culverts,  arch  centering,  piers,  etc. 
These  are  from  current  periodicals  and  show  actual  struc- 
tures. 

BECAUSE — it  contains  over  160  pages  of  information  on 
the  properties  and  use  of  cement,  concrete,  steel,  etc.,  fin- 
ishing of  concrete  surfaces,  designing  forms,  and  other 
practical  information. 

BECAUSE — the  theoretical  portion  is  given  in  the  sim- 
plest possible  manner,  at  the  same  time  being  as  thorough 
ac  the  materials  demand. 

152 


BECAUSE — the  reader  is  treated  as  a  reasoning  being  and 
not  a  child  to  accept  dogma  and  "say  so." 

BECAUSE — "It  contains  a  large  amount  of  very  good  ma- 
terial" Engineering-Contracting,  May  6,  '08. 

BECAUSE — "A  thorough  exposition  of  the  properties  of 
concrete  and  cement  is  given.  *  *  To  those  unfamiliar  with 
Mr.  Godfrey's  articles  *  *  *  this  work  will  prove  interest- 
ing and  valuable  reading.  The  rather  novel  method  which 
he  uses  *  *  makes  the  book  valuable  *  *  and  adds  an  ele- 
ment of  interest  to  the  reading  that  practicalfy  all  techni- 
cal works  lack.  Altogether  Mr.  Godfrey's  work  is  a  valu- 
able contribution  to  the  literature  of  concrete  and  concrete 
engineering."  Engineering  Digest,  May,  '08. 

BECAUSE — "It  has  a  truly  flexible  back,  is  printed  on  good 
paper,  and  the  workmanship  is  first  class.  *  *  The  book  is 
full  of  meat  and  good  things.  *  *  There  is  a  lot  of  spice  in 
it.  *  *  The  book  has  so  much  of  good  in  it  that  every  man 
who  possesses  a  satisfying  amount  of  knowledge  of  rein- 
forced concrete  will  enjoy  reading  it.  The  handy  pocket 
size  and  good  binding  make  it  a  book  one  can  take  on  the 
cars  to  read." — The  Contractor,  April,  '08. 

BECAUSE — "The  text  is  written  straight  to  the  point, 
free  from  unnecessary  technicalities  and  full  of  practical 
points.  The  tables  and  illustrations  are  of  value,  and  the 
book  at  its  price  should  prove  an  excellent  investment  to 
the  worker  in  reinforced  concrete,  whether  he  is  engin- 
eer, foreman  or  designer." — Concrete,  April,  '08. 

BECAUSE — "In  his  theory  the  author  is  sound." — Engin- 
eering News,  May  14,  '08. 

BECAUSE — the  price  is  only  $2.50  net. 

WHY  EVERY  MAN  WHO  IS  INTERESTED  IN 
THE  DESIGN  OF  STEEL  STRUCTURES  SHOULD 
HAVE  A  COPY  OF 

GODFREY'S  TABLES. 

BECAUSE— it  is  the  best  book  of  its  kind  in  the  English 
language. 

"The  author  of  these  Tables'  has  produced  a  work  that 
is  in  many  respects  distinctly  ahead  of  anything  yet  pub- 
lished in  the  English  language.  *  *  As  a  whole  the  book 
represents  a  very  useful  collection  of  structural  tables,  and 
a  very  compact  one." — Engineering  News. 


153 


Godfrey's   Tables 

[Structural  Engineering,  Book  One] 

This  book  is  a  compilation  of  tables  and  data  for 
use  in  structural  designing.  About  one-third  of  it  is 
collected  from  manufacturer's  hand-books  and  includes 
such  data  as  the  properties  of  rolled  sections,  standards 
for  bolts  and  rivets,  eyebar  tables,  fractions  to  decimals, 
and  other  tables  common  to  many  books  and  indespen- 
sable  to  the  designer.  Besides  the  foregoing  there  is 
more  new  matter  in  the  book  than  in  any  other  simi- 
lar book  published.  There  is  scarcely  a  problem  in  struc- 
tural designing  or  detailing  in  which  this  book  will  not 
be  found  useful. 

The  book  contains  more  than  200  pages.  Following 
is  a  list  of  the  contents:  Decimals  of  a  foot  and  inch. 
Properties  and  useful  dimensions  of  beams,  channels, 
angles,  zees,  tees,  rails.  Information  on  eyebars, 
clevises,  sleevenuts,  separators,  nuts,  rivets,  bolts,  cir- 
cular and  rectangular  plates,  corrugated  and  buckled 
plates.  Standard  beam  connections.  Bending  moments 
on  beams  for  concentrated  and  uniform  loads.  Deflec- 
tion formulas  in  terms  of  fibre  stress,  new.  Working 
unit  stresses  on  columns.  Ultimate  strength  of  tank 
plates,  new.  Weights  of  substances.  Conversion  table 
for  French  units.  Moments  of  inertia  of  rectangles 
varying  by  eights,  new.  Weights  and  areas  of  rods, 
bars,  and  plates.  Mensuration,  lengths  of  curves  and 
areas  if  segments,  new.  Miscellaneous  formulas  in 
usable  shape  (brake  bands,  hoops,  cylinders,  springs, 
flat  plates,  R.  R.  curves,  etc.)  Skewdetails,  hip  and  val- 
ley details,  no  angles  used,  new.  Stresses  in  eight 
styles  of  roof  trusses,  four  pitches  each.  Moments, 
shears,  etc.,  Cooper  E  50  loading  Tables  of  built  girders, 
new.  Over  2000  built  sections  with  their  properties. 
Functions  of  angles.  Typical' details,  38  pages.  Tables 
of  roots  and  circular  areas.  Tables  of  squares  of  num- 
bers to  2736.  Tables  of  squares  of  feet,  inches,  and 
fractions  for  finding  hypothenuse,  lengths  to  57  feet, 
new.  Gears,  chain,  rope.  Electric  cranes,  clearances, 
loads,  etc. 

All  of  this  in  a  small  pocktbook.  Could  anything  be 
more  useful  to  a  structural  designer,  draftsman  or  stu- 
dent? 


154 


JNO.    J.    CONE 


•  ROBERT    W.    HUNT 

D.  w.  MCNAUGHER 


JAS.    C.    HALLSTED 


ROBERT  W.  HUNT  4  CO, 

ENGINEERS 

BUREAU  OF  INSPECTION,  TESTS 
AND  CONSULTATION 


Thoroughly    equipped    Chemical   and    Physical 
Laboratories  maintained  at 

Chicago,  New  York,  San  Francisco  4  London. 

Inspection  and  tests  of  Rails  and  Fastenings, 
Locomotives,  Cars,  Pipe,  Bridges,  Buildings, 
Machinery  and  2nd  hand  equipment. 

Examination  and  reports  on  existing  structures. 
Reviews  of  metal  and  concrete-steel  construction. 

CHICAGO  :    1121  The  Rookery 

NEW  YORK :  PITTSBURG  : 

90  West  Street  Monongahela  Bank  Building 

LONDON  :  Norfolk  House,  Cannon  Street,  E.  C. 

MONTREAL:  SAN  FRANCISCO  : 

Board  of  Trade  Building  425  Washington  Street 

155 


GODFREY  PATENT 
RETAINING   WALL 

6B68 

See  Engineering  News,  Oct.  18,  1906. 

See  Engineering-Contracting,  Dec.  21,  1910. 

See  Engineering-Contracting,  Jan.  18,  1911. 


\ 


A  complete  description  of  this  retaining  wall  will  be 
found  in  the  above  references,  as  well  as  the  method  of 
designing  such  walls.  This  is  the  safest  design  for  rein- 
forced concrete  retaining  walls  that  is  before  the  public. 
It  is  also  economical.  For  further  information  address 
Edward  Godfrey,  Monongahela  Bank  Building,  Pittsburg, 
Penn'a. 

156 


II 

£5 

QZi 

o 

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UNIVERSITY  OF  CALIFORNIA  LIBRARY 


